Generic models for genus 2 curves with real multiplication
Alex Cowan, Sam Frengley, Kimball Martin arXiv:2403.03191
Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds
Noam Elkies
Rational torsion points on abelian surfaces with quaternionic multiplication
Jef Laga, Ciaran Schembri, Ari Shnidman, and John Voight arXiv:2308.15193
On abelian varieties whose torsion is not self-dual
Sarah Frei, Katrina Honigs, and John Voight arXiv:arXiv:2309.00531
Trace formulas for the norm one group of totally definite quaternion algebras
Jiangwei Xue and Chia-Fu Yu (with an appendix by John Voight) arXiv:1909.11858
Ideal classes of orders in quaternion algebras
Stefano Marseglia, Harry Smit, and John Voight,
Kneser’s method of neighbors
John Voight
Murmurations of modular forms in the weight aspect
Jonathan Bober, Andrew R. Booker, Min Lee, David Lowry-Duda arXiv:2310.07746
Counting Divisors in the Outputs of a Binary Quadratic Form
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker, Tinghao Huang arXiv:2310.13632
Towards a classification of isolated j-invariants
Abbey Bourdon, Sachi Hashimoto, Timo Keller, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, Himanshu Shukla arXiv:2311.07740
Rationality of forms of \bar{M}_{0,n}
Brendan Hassett, Yuri Tschinkel, Zhijia Zhang arXiv:2402.03062
The automorphisms of certain Kummer surfaces act on the points mod p by the alternating group
Adam Logan, Owen Patashnick arXiv:2311.04353
The Brauer group of $\mathcal(Y)_0(2)$
N. Achenjang, D. Bhamidipati, A. Jha, C. Ji, R. Lopez arXiv:2311.18132
Integral Points on elliptic curves over imaginary quadratic fields
A. Jha arXiv:2311.01691
Coleman Integration on Modular Curves
M. Chen, K. Kedlaya, and J. Lau arXiv:2401.14513
A census of genus 6 curves over F_2
Y. Huang, K. Kedlaya, and J. Lau arXiv:2402.00716
Local heights on hyperelliptic curves and quadratic Chabauty
A. Betts, J. Duque-Rosero, S. Hashimoto, and P. Spelier arXiv:2401.05228
The classifying element for quotients of Fermat curves
J. Duque-Rosero and R. Pries arXiv:2312.07710
On invariants of Artin-Schreier curves
J. Duque-Rosero, H. Goodson, E. Lorenzo García, B. Malmskog, and R. Scheidler arXiv:2401.08843
Linear x-coordinate relations of triples on elliptic curves
J. Caro and N. Garcia-Fritz arXiv:2310.17592
Torsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville
B. Banwait and M. Derrick arXiv:2401.14514
Computing Euler factors of genus 2 curves at odd primes of almost good reduction
C. Maistret and A.V. Sutherland arXiv:2402.02271
Equations of genus 4 curves from their theta constants
J. Hanselman, A. Pieper, and S. Schiavone arXiv:2402.03160
Hypergeometric L-functions in average polynomial time, II
E. Costa, K.S. Kedlaya, D. Roe arXiv:2310.06971
Mod p Galois representations not arising from abelian varieties
S. Chidambaram arXiv:2011.00158
Doubly isogenous curves of genus two with a rational action of D_6
J. Booher, E.W. Howe, A.V. Sutherland, and J.F. Voloch arXiv:2402.08853
Reduction of Plane Quartics and Dixmier-Ohno invariants
R. van Bommel, J. Docking, R. Lercier, and E. Lorenzo García arXiv:2309.17381
Counting Divisors in the Outputs of a Binary Quadratic Form
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker, Tinghao Huang arXiv:2310.13632
Murmurations of modular forms in the weight aspect
Jonathan Bober, Andrew R. Booker, Min Lee, David Lowry-Duda arXiv:2310.07746
Reduction of Plane Quartics and Cayley Octads
Raymond van Bommel, Jordan Docking, Vladimir Dokchitser, Reynald Lercier, Elisa Lorenzo García arXiv:2309.17381
Dimension formulas for spaces of vector-valued Siegel modular forms of degree two and level two
Jonas Bergström, Fabien Cléry arXiv:2309.04388
Obstructions to applying the Baker–Bilu method for determining integral points on curves
Aaron Landesman and Bjorn Poonen arXiv:2306.11799
Computing the endomorphism ring of an elliptic curve over a number field
John E. Cremona and Andrew V. Sutherland arXiv:2301.11169
Fekete polynomials of principal Dirichlet characters
Shiva Chidambaram, Ján Mináč, Tung T. Nguyen, and Nguyen Duy Tân arXiv:2307.14896
Creating a Database of Finite Groups
Lewis Combes, John Jones, Jennifer Paulhus, David Roe, Manami Roy, and Sam Schiavone
Computing torsion for plane quartics without using height bounds
Raymond van Bommel arXiv:2301.08312
Geometric quadratic Chabauty and p-adic heights
Juanita Duque-Rosero, Sachi Hashimoto, and Pim Spelier arXiv:2207.10389
A census of cubic fourfolds over F_2
Asher Auel, Avinash Kulkarni, Jack Petok, and Jonah Weinbaum arXiv:2306.09908
A database of paramodular forms from quinary orthogonal modular forms
Eran Assaf, Watson Ladd, Gustavo Rama, Gonzalo Tornaria, and John Voight arXiv:2308.09824
Monodromy groups of Jacobians with definite quaternionic multiplication
Victoria Cantoral-Farfán, Davide Lombardo, and John Voight arXiv:2303.00804
Counting elliptic curves over the rationals with a 7-isogeny
Grant Molnar and John Voight arXiv:2212.11354
Explicit isogenies of prime degree over number fields
Barinder S. Banwait and Maarten Derickx arXiv:2203.06009
Modularity over C implies modularity over Q
Barinder S. Banwait arXiv:2212.14412
Towards strong uniformity for isogenies of prime degree
Barinder S. Banwait and Maarten Derickx arXiv:2302.08350
Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves
Oana Padurariu and Ciaran Schembri arXiv:2212.04553
Rational points on rank 2 genus 2 bielliptic curves in the LMFDB
Francesca Bianchi and Oana Padurariu arXiv:2212.11635
Ogg’s Torsion conjecture: Fifty years later
Jennifer S. Balakrishnan and Barry Mazur arXiv:2307.04752
Murmurations and explicit formulas
Alex Cowan arXiv:2306.10425
A twisted additive divisor problem
Alex Cowan arXiv:2304.12572
Statistics of modular forms with small rationality fields
Alex Cowan and Kimball Martin arXiv:2301.10357
Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
Raymond van Bommel, Shiva Chidambaram, Edgar Costa, and Jean Kieffer arXiv:2301.10118
A database of basic numerical invariants of Hilbert modular surfaces
Eran Assaf, Angelica Babei, Ben Breen, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone, and John Voight arXiv:2301.10302
Chabauty-Kim and the Section Conjecture for locally geometric sections
L. Alexander Betts, Theresa Kumpitsch, and Martin Lüdtke arXiv:2305.09462
p-adic adelic metrics and Quadratic Chabauty I
Amnon Besser, J.Steffen Mueller, and Padmavathi Srinivasan arXiv:2112.03873
Quadratic enrichments of the logarithmic derivative of the zeta function
Margaret Bilu, Wei Ho, Padmavathi Srinivasan, Isabel Vogt, and Kirsten Wickelgren arXiv:2210.03035
Conductor-discriminant inequality for hyperelliptic curves in odd residue characteristic
Andrew Obus, Padmavathi Srinivasan arXiv:1910.02589
Computing nonsurjective primes associated to Galois representations of genus 2 curves
Barinder S. Banwait, Armand Brumer, Hyun Jong Kim, Zev Klagsbrun, Jacob Mayle, Padmavathi Srinivasan, and Isabel Vogt arXiv:2301.02222
Integrable Lagrangians and Picard modular forms
Fabien Cléry, Evgeny V. Ferapontov, Alexander Odesskii, and Don Zagier
Sums of Cusp Form Coefficients Along Quadratic Sequences
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker, Raphael S. Steiner arXiv:2301.11901
Modular forms via invariant theory
Fabien Cléry and Gerard van der Geer arXiv:2211.05611
Involutions on K3 surfaces and derived equivalence
Brendan Hassett and Yuri Tschinkel arXiv:2303.03294
Sums of Cusp Form Coefficients Along Quadratic Sequences
Chan Ieong Kuan, David Lowry-Duda, Alexander Walker arXiv:2301.11901
Counting points on abelian surfaces over finite fields with Elkies’s method
Jean Kieffer arXiv:2203.02009
Certified Newton schemes for the evaluation of low-genus theta functions
Jean Kieffer arXiv:2203.02000
Towards Uniform Chabauty–Kim
L. Alexander Betts, David Corwin, Marius Leonhardt arXiv:2206.11085
Galois sections and p-adic period mappings
L. Alexander Betts, Jakob Stix arXiv:2204.13674
Local constancy of pro-unipotent Kummer maps
L. Alexander Betts arXiv:2203.03701
Moduli for rational genus 2 curves with real multiplication for discriminant 5
Alex Cowan, Kimball Martin arXiv:2206.05752
Non-Random Behaviour in Sums of Modular Symbols
Alexander Cowan arXiv:1905.10743
Appendix A: Jacobians of arbitrary modular curves to ℓ-adic images of Galois for elliptic curves over ℚ
Jeremy Rouse, Andrew V. Sutherland, John Voight, David Zureick-Brown arXiv:2106.11141
Computing Euclidean Belyi maps
Matthew Radosevich, John Voight arXiv:2111.07504
Triangular modular curves of low genus
Juanita Duque-Rosero, John Voight arXiv:2203.08593
Stickelberger’s discriminant theorem for algebras
Asher Auel, Owen Biesel, John Voight arXiv:2208.06138
On smooth plane models for modular curves of Shimura type
Samuele Anni, Eran Assaf, Elisa Lorenzo García arXiv:2203.06370
Rationality of twists of the Siegel modular variety of genus 2 and level 3
Frank Calegari and Shiva Chidambaram arXiv:2009.00194
Arithmetic Geometry, Number Theory, and Computation
J. Balakrishnan, N. Elkies, B. Hassett, B. Poonen, A. Sutherland, and J. Voight
Cyclic isogenies of elliptic curves over a fixed quadratic field
Barinder S. Banwait, Filip Najman, Oana Padurariu arXiv:2206.08891
A Study of Error Floor Behavior in QC-MDPC Codes
Sarah Arpin, Raven Billingsley, Daniel Rayor Hast, Jun Bo Lau, Ray Perlner, Angela Robinson
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver, David Lowry-Duda, George Shakan, Ruixiang Zhang arXiv:2107.02914
The relative class number one problem for function fields, I
Kiran S. Kedlaya arXiv:2202.08382
Explicit two-cover descent for genus 2 curves
Daniel Rayor Hast arXiv:2009.10313
A deterministic algorithm for finding r-power divisors
David Harvey, Markus Hittmeir arXiv:2202.12401
On Powerful Integers Expressible As Sums Of Two Coprime Fourth Powers
Noam D. Elkies and Gaurav Goel
Counting Points On Smooth Plane Quartics
Edgar Costa, David Harvey, and Andrew V. Sutherland arXiv:2208.09890
On the vanishing of twisted L-functions of elliptic curves over rational function fields
Antoine Comeau-Lapointe, Chantal David, Matilde Lalin, Wanlin Li arXiv:2207.00197
Definite orthogonal modular forms: Computations, Excursions and Discoveries
Eran Assaf, Dan Fretwell, Colin Ingalls, Adam Logan, Spencer Secord, John Voight arXiv:2203.06405
On smooth plane models for modular curves of Shimura type
Samuele Anni, Eran Assaf, Elisa Lorenzo García arXiv:2203.06370
Rational Points On Hyperelliptic Atkin-Lehner Quotients Of Modular Curves And Their Coverings
Nikola Adžaga, Shiva Chidambaram, Timo Keller, Oana Padurariu arXiv:2203.05541
Towards Flying through Modular Forms
David Lowry-Duda, Adam Sakareassen arXiv:2104.15116
Improved bounds on number fields of small degree
Theresa C. Anderson, Ayla Gafni, Kevin Hughes, Robert J. Lemke Oliver, David Lowry-Duda, Frank Thorne, Jiuya Wang, Ruixiang Zhang arXiv:2204.01651
Prime Sums
Anupam Datta, Nir Elber, Raymond Feng, David Lowry-Duda, Henry Xie arXiv:2111.02795
Sign changes of cusp form coefficients on indices that are sums of two squares
David Lowry-Duda arXiv:2108.12520
Generating Picard modular forms by means of invariant theory
Fabien Cléry, Gerard van der Geer arXiv:2110.00849
Zen and the art of database maintenance
Edgar Costa and David Roe
From the Birch and Swinnerton-Dyer conjecture to Nagao’s conjecture
S. Kim and R. Murty arXiv:2105.10805v3
ℓ-adic images of Galois for elliptic curves over ℚ
J. Rouse, D. Zureick-Brown, and A.V. Sutherland arXiv:2106.11141v2
Commutative character sheaves and geometric types for supercuspidal representations
C. Cunningham and D. Roe arXiv:1605.08820v4
Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6
N. Adžaga, V. Arul, L. Beneish, M. Chen, S. Chidambaram, T. Keller, and B. Wen arXiv:2105.04811v1
Dual linear programming bounds for sphere packing via modular forms
H. Cohn and N. Triantafillou arXiv:1909.04772
The unit equation has no solutions in number fields of degree prime to 3 where 3 splits completely
N. Triantafillou arXiv:2003.02414
A Prym variety with everywhere good reduction over ℚ(61‾‾‾√)
N. Mascot, J. Sijsling, and J. Voight arXiv:1908.00421
The L-Functions and Modular Forms Database
J. Cremona, J. Jones, A. Sutherland, and J. Voight
On basic and Bass quaternion orders
S. Chari, D. Smertnig, and J. Voight arXiv:1903.00560
Existence of invariant norms in p-adic representations of GL2(F) of large weights
E. Assaf arXiv:1711.06314
Rational points on solvable curves over ℚ via non-abelian Chabauty
Jordan S. Ellenberg, Daniel Rayor Hast arXiv:1706.00525
The valuation of the discriminant of a hypersurface
Bjorn Poonen, Michael Stoll
Lattices in Tate modules
Bjorn Poonen, Sergey Rybakov arXiv:2107.06363
Introduction to Drinfeld modules
Bjorn Poonen
The proportion of derangements characterizes the symmetric group
Bjorn Poonen, Kaloyan Slavov arXiv:2107.02724
Abelian varieties of prescribed order over finite fields
Raymond van Bommel, Edgar Costa, Wanlin Li, Bjorn Poonen, Alexander Smith arXiv:2106.13651
The S-integral points on the projective line minus three points via finite covers and Skolem’s method
Bjorn Poonen
Equivariant geometry of odd-dimensional complete intersections of two quadrics
Brendan Hassett, Yuri Tschinkel arXiv:2107.14319
Sporadic Cubic Torsion
Maarten Derickx, Anastassia Etropolski, Mark van Hoeij, Jackson S. Morrow, David Zureick-Brown arXiv:2007.13929
Abelian varieties over 2 of prescribed order
Kiran S. Kedlaya arXiv:2107.12453
Every positive integer is the order of an ordinary abelian variety over 2
Everett W. Howe, Kiran S. Kedlaya arXiv:2103.16530v3
Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants
Theresa C. Anderson, Ayla Gafni, Robert J. Lemke Oliver, David Lowry-Duda, George Shakan, Ruixiang Zhang arXiv:2107.02914
Sato-Tate groups of abelian threefolds
Francesc Fité, Kiran S. Kedlaya, Andrew V. Sutherland arXiv:2106.13759
Higher spectral sequences
Benjamin Matschke arXiv:2107.02130
Data for Shimura varieties intersecting the Torelli locus
Wanlin Li, Elena Mantovan, Rachel Pries arXiv:2105.02286
Stronger arithmetic equivalence
Andrew V. Sutherland arXiv:2104.01956
Quadratic Fields Admitting Elliptic Curves with Rational j-Invariant and Good Reduction Everywhere
Benjamin Matschke, Abhijit S. Mudigonda arXiv:2103.09814
Doubly isogenous genus-2 curves with D4-action
Vishal Arul, Jeremy Booher, Steven R. Groen, Everett W. Howe, Wanlin Li, Vlad Matei, Rachel Pries, Caleb Springer arXiv:2102.11419
Even values of Ramanujan’s tau-function
Jennifer S. Balakrishnan, Ken Ono, Wei-Lun Tsai arXiv:2102.00111
Rationality of even-dimensional intersections of two real quadrics
Brendan Hassett, János Kollár, Yuri Tschinkel arXiv:2101.08931
An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process
Eran Assaf, Jeremiah Buckley, Naomi Feldheim arXiv:2101.04052
Quadratic Chabauty for modular curves: Algorithms and examples
Jennifer S. Balakrishnan, Netan Dogra, Jan Steffen Müller, Jan Tuitman, Jan Vonk arXiv:2101.01862
Vanishing of Dirichlet L-functions at the central point over function fields
Ravi Donepudi, Wanlin Li arXiv:2012.15319
Space vectors forming rational angles
Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, Michael Rubinstein arXiv:2011.14232
Computing integral points on X_ns^+(p)
Aurélien Bajolet, Yuri Bilu, Benjamin Matschke arXiv:1212.0665
Computing newforms using supersingular isogeny graphs
Alex Cowan arXiv:2010.10745
Symbols and equivariant birational geometry in small dimensions
Brendan Hassett, Andrew Kresch, Yuri Tschinkel arXiv:2010.08902
Surface bundles and the section conjecture
Wanlin Li, Daniel Litt, Nick Salter, Padmavathi Srinivasan arXiv:2010.07331
Computing L-Polynomials of Picard curves from Cartier-Manin matrices
Sualeh Asif, Francesc Fité, Dylan Pentland arXiv:2010.07247
A general S-unit equation solver and tables of elliptic curves
Benjamin Matschke
The Ceresa class: tropical, topological, and algebraic
Daniel Corey, Jordan Ellenberg, Wanlin Li arXiv:2009.10824
Explicit two-cover descent for genus 2 curves
Daniel Rayor Hast arXiv:2009.10313
Conjecture: 100% of elliptic surfaces over ℚ have rank zero
Alex Cowan arXiv:2009.08622
Square root time Coleman integration on superelliptic curves
Alex J. Best
Modular forms of degree 2 and curves of genus 2 in characteristic 2
Fabien Cléry, Gerard van der Geer arXiv:2003.00249
Super-linear convergence in the p-adic QR-algorithm
Avinash Kulkarni, Tristan Vaccon arXiv:2009.00129
Etale and crystalline companions, II
Kiran S. Kedlaya arXiv:2008.13053
The Chabauty–Coleman method and p-adic linear forms in logarithms
Netan Dogra arXiv:2008.09560
The Distribution Relation and Inverse Function Theorem in Arithmetic Geometry
Yohsuke Matsuzawa, Joseph H. Silverman arXiv:2008.08149
Bounds on the Torsion Subgroup Schemes of Néron-Severi Group Schemes
Hyuk Jun Kweon arXiv:2008.01908
Arithmetic Progressions of Squares and Multiple Dirichlet Series
Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, Alexander Walker arXiv:2007.14324
Deep Learning Gauss-Manin Connections
Kathryn Heal, Avinash Kulkarni, Emre Can Sertöz arXiv:2007.13786
Elliptic curves with good reduction outside of the first six primes
Alex J. Best, Benjamin Matschke arXiv:2007.10535
A user’s guide to the local arithmetic of hyperelliptic curves
Alex J. Best, L. Alexander Betts, Matthew Bisatt, Raymond van Bommel, Vladimir Dokchitser, Omri Faraggi, Sabrina Kunzweiler, Céline Maistret, Adam Morgan, Simone Muselli, Sarah Nowell arXiv:2007.01749v3
On a question of Mordell
Andrew R. Booker, Andrew V. Sutherland arXiv:2007.01209
What is…a Coleman integral?
Jennifer S. Balakrishnan
Restriction of Scalars Chabauty and the S-Unit Equation
Nicholas Triantafillou arXiv:2006.10590
A p-adic approach to rational points on curves
Bjorn Poonen arXiv:2006.01774
The local-global principle for integral points on stacky curves
Manjul Bhargava, Bjorn Poonen arXiv:2006.00167
Hypergeometric L-functions in average polynomial time
Edgar Costa, Kiran S. Kedlaya, David Roe arXiv:2005.13640
Ordinary primes for some varieties with extra endomorphisms
Francesc Fité arXiv:2005.10185
A Topology on Points on Stacks
Atticus Christensen arXiv:2005.10231
Variants of Lehmer’s speculation for newforms
Jennifer S. Balakrishnan, William Craig, Ken Ono, Wei-Lun Tsai arXiv:2005.10354
Variations of Lehmer’s Conjecture for Ramanujan’s tau-function
Jennifer S. Balakrishnan, William Craig, Ken Ono arXiv:2005.10345
On a probabilistic local-global principle for torsion on elliptic curves
John Cullinan, Meagan Kenney, John Voight arXiv:2005.06669
Linear independence in linear systems on elliptic curves
Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen, Anthony J. Scholl, Joseph L. Wetherell arXiv:2005.05473
Gluing curves of genus 1 and 2 along their 2-torsion
Jeroen Hanselman, Sam Schiavone, Jeroen Sijsling arXiv:2005.03587
A Canonical Form for Positive Definite Matrices
Mathieu Dutour Sikirić, Anna Haensch, John Voight, Wessel P.J. van Woerden arXiv:2004.14022
Counting points on superelliptic curves in average polynomial time
Andrew V. Sutherland arXiv:2004.10189
Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class
Dean Bisogno, Wanlin Li, Daniel Litt, Padmavathi Srinivasan arXiv:2004.06146
Effective obstruction to lifting Tate classes from positive characteristic
Edgar Costa, Emre Can Sertöz arXiv:2003.11037
Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB
Taylor Dupuy, Kiran Kedlaya, David Roe, Christelle Vincent arXiv:2003.05380
Counterexamples to a Conjecture of Ahmadi and Shparlinski
Taylor Dupuy, Kiran Kedlaya, David Roe, Christelle Vincent arXiv:2003.05368
The unit equation has no solutions in number fields of degree prime to 3 where 3 splits completely
Nicholas Triantafillou arXiv:2003.02414
New Rank Records For Elliptic Curves Having Rational Torsion
Noam D. Elkies, Zev Klagsbrun arXiv:2003.00077
Effective Sato-Tate conjecture for abelian varieties and applications
Alina Bucur, Francesc Fité, Kiran S. Kedlaya arXiv:2002.08807
38406501359372282063949 & all that: Monodromy of Fano Problems
Sachi Hashimoto, Borys Kadets arXiv:2002.04580
Visualizing modular forms
David Lowry-Duda arXiv:2002.05234
Computational tools for quadratic Chabauty (lecture notes for the 2020 Arizona Winter School)
Jennifer S. Balakrishnan, J. Steffen Müller
Efficient computation of BSD invariants in genus 2
Raymond van Bommel arXiv:2002.04667
Computing classical modular forms
Alex J. Best, Jonathan Bober, Andrew R. Booker, Edgar Costa, John Cremona, Maarten Derickx, David Lowry-Duda, Min Lee, David Roe, Andrew V. Sutherland, John Voight arXiv:2002.04717
Restrictions on Weil polynomials of Jacobians of hyperelliptic curves
Edgar Costa, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, Caleb Springer, Mckenzie West arXiv:2002.02067
Congruent number triangles with the same hypotenuse
David Lowry-Duda arXiv:2002.01024
The exceptional locus in the Bertini irreducibility theorem for a morphism
Bjorn Poonen, Kaloyan Slavov arXiv:2001.08672
Frobenius structures on hypergeometric equations
Kiran S. Kedlaya arXiv:1912.13073
Sato-Tate groups of abelian threefolds: a preview of the classification
Francesc Fité, Kiran S. Kedlaya, Andrew V. Sutherland arXiv:1911.02071
Triple Correlation Sums of Coefficients of Cusp Forms
Thomas Hulse, Chan Ieong Kuan, David Lowry-Duda, Alexander Walker arXiv:1911.09216
Parity conjecture for abelian surfaces
Vladimir Dokchitser, Celine Maistret arXiv:1911.04626
Functional transcendence for the unipotent Albanese map
Daniel Rayor Hast arXiv:1911.00587
On the ℓ-adic valuation of certain Jacobi sums
Vishal Arul arXiv:1910.14249
Torsion points on Fermat quotients of the form yn=xd+1
Vishal Arul arXiv:1910.14251
Rationality of Fano threefolds of degree 18 over nonclosed fields
Brendan Hassett, Yuri Tschinkel arXiv:1910.13816
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi, Brian Lawrence, J. Steffen Müller, Nicholas Triantafillou, Jan Vonk arXiv:1910.12755
Post-Critically Finite Maps on ℙn for n≥2 are Sparse
Patrick Ingram, Rohini Ramadas, Joseph H. Silverman arXiv:1910.11290
Non-real Poles and Irregularity of Distribution
David Lowry-Duda arXiv:1910.09969
Explicit quadratic Chabauty over number fields
Jennifer S. Balakrishnan, Amnon Besser, Francesca Bianchi, J. Steffen Müller arXiv:1910.04653
Arithmetic invariants from Sato–Tate moments
Edgar Costa, Francesc Fité, Andrew V. Sutherland arXiv:1910.00518
On unit signatures and narrow class groups of odd abelian number fields: structure and heuristics
Benjamin Breen, Ila Varma, John Voight, appendix with Noam Elkies arXiv:1910.00449
Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of GL2-type
Francesc Fité, Xavier Guitart arXiv:1909.11712
Periodic continued fractions over S-integers in number fields and Skolem’s p-adic method
Bradley W. Brock, Noam D. Elkies, Bruce W. Jordan arXiv:1909.11214
Ramification of étale path torsors and harmonic analysis on graphs
L. Alexander Betts, Netan Dogra arXiv:1909.05734
Proofs by example
Benjamin Matschke arXiv:1909.00480
p-adic Integral Geometry
Avinash Kulkarni, Antonio Lerario arXiv:1908.04775
Cycle class maps and birational invariants
Brendan Hassett, Yuri Tschinkel arXiv:1908.00406
A Prym variety with everywhere good reduction over ℚ(√61)
Nicolas Mascot, Jeroen Sijsling, John Voight arXiv:1908.00421
On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
John Cremona, Lassina Dembélé, Ariel Pacetti, Ciaran Schembri, John Voight arXiv:1907.12103
Solving p-adic polynomial systems via iterative eigenvector algorithms
Avinash Kulkarni arXiv:1907.03740
Linear Dependence Among Hecke Eigenvalues
Dohyeong Kim
Ramification in the Cohomology of Algebraic Surfaces Arising from Ordinary Double Point Singularities
Dohyeong Kim
Quadratic Chabauty for modular curves and modular forms of rank one
Netan Dogra, Samuel Le Fourn arXiv:1906.08751
Special hypergeometric motives and their L-functions: Asai recognition
Lassina Dembélé, Alexei Panchishkin, John Voight, Wadim Zudilin arXiv:1906.07384
Counting elliptic curves with an isogeny of degree three
Maggie Pizzo, Carl Pomerance, John Voight arXiv:1906.07877
An intriguing hyperelliptic Shimura curve quotient of genus 16
Lassina Dembele arXiv:1906.06772
A homotopy Lie formula for the p-adic Dwork Frobenius operator
Dohyeong Kim, Jeehoon Park, Junyeong Park arXiv:1906.06564
Estimates for the number of rational points on simple abelian varieties over finite field
Borys Kadets arXiv:1906.02264
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
Edgar Costa, Davide Lombardo, John Voight arXiv:1906.02803
When Are There Continuous Choices for the Mean Value Abscissa?
David Lowry-Duda, Miles H. Wheeler arXiv:1906.02026
Explicit arithmetic intersection theory and computation of Néron-Tate heights
Raymond van Bommel, David Holmes and J. Steffen Müller arXiv:1809.06791
Varieties of planes on intersections of three quadrics
Brendan Hassett, Yuri Tschinkel arXiv:1904.06313
Definite orders with locally free cancellation
Daniel Smertnig, John Voight arXiv:1903.10662
On the existence of abelian surfaces with everywhere good reduction
Lassina Dembele arXiv:1903.10394
Rationality of complete intersections of two quadrics
Brendan Hassett, Yuri Tschinkel arXiv:1903.08979
Unlikely intersections and the Chabauty-Kim method over number fields
Netan Dogra arXiv:1903.05032
Moduli Spaces for Dynamical Systems with Portraits
John R. Doyle, Joseph H. Silverman arXiv:1812.09936
Multiplicative dependence among iterated values of rational functions modulo finitely generated groups
Attila Bérczes, Alina Ostafe, Igor E. Shparlinski, Joseph H. Silverman arXiv:1811.04971
Nonvanishing of hyperelliptic zeta functions over finite fields
Jordan S. Ellenberg, Wanlin Li, Mark Shusterman arXiv:1901.08202
Elliptic Curves over Totally Real Cubic Fields are Modular
Maarten Derickx, Filip Najman, Samir Siksek arXiv:1901.03436
Etale and crystalline companions, I
Kiran S. Kedlaya arXiv:1811.00204
Division by 1−ζ on superelliptic curves and jacobians
Vishal Arul arXiv:1810.07299
Specialization of Néron-Severi groups in characteristic p
Atticus Christensen arXiv:1810.06550
Hypergeometric decomposition of symmetric K3 quartic pencils
Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher arXiv:1810.06254
The Inverse Galois Problem for p-adic fields
David Roe arXiv:1809.10195
A Database of Belyi Maps
Michael Musty, Sam Schiavone, Jeroen Sijsling, John Voight arXiv:1805.07751
Endomorphism algebras of geometrically split abelian surfaces over ℚ
Francesc Fité, Xavier Guitart arXiv:1807.10010
Archimedean local height differences on elliptic curves
J. Steffen Müller, Corinna Stumpe arXiv:1807.04153
On the Hilbert eigenvariety at exotic and CM classical weight 1 points
Adel Betina, Shaunak V. Deo, Francesc Fité arXiv:1806.11540
A database of nonhyperelliptic genus 3 curves over Q
Andrew V. Sutherland arXiv:1806.06289
Mod-2 dihedral Galois representations of prime conductor
Kiran S. Kedlaya, Anna Medvedovsky arXiv:1806.04653
Explicit Coleman Integration in Larger Characteristic
Alex J. Best arXiv:1806.03393
Computing Zeta Functions of Cyclic Covers in Large Characteristic
Vishal Arul, Alex J. Best, Edgar Costa, Richard Magner, Nicholas Triantafillou arXiv:1806.02262
Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology
Edgar Costa, David Harvey, Kiran S. Kedlaya arXiv:1806.00368
Modular eigenforms at the boundary of weight space
Jan Vonk
A database of Hilbert modular forms
Steve Donnelly, John Voight arXiv:1605.02637
On the paramodularity of typical abelian surfaces
Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight, David S. Yuen arXiv:1805.10873
Chabauty-Coleman experiments for genus 3 hyperelliptic curves
Jennifer S. Balakrishnan, Francesca Bianchi, Victoria Cantoral-Farfán, Mirela Çiperiani, Anastassia Etropolsk arXiv:1805.03361
An effective Chabauty-Kim theorem
Jennifer Balakrishnan, Netan Dogra arXiv:1803.10102
ZpL: a p-adic precision package
Xavier Caruso, David Roe, Tristan Vaccon arXiv:1802.08532
Stable rationality in smooth families of threefolds
Brendan Hassett, Andrew Kresch, Yuri Tschinkel arXiv:1802.06107
Quadrilaterals inscribed in convex curves
Benjamin Matschke arXiv:1801.01945
Sato-Tate distributions of twists of the Fermat and the Klein quartics
Francesc Fité, Elisa Lorenzo García, and Andrew V. Sutherland arXiv:1712.07105
The Belyi degree is computable
Ariyan Javanpeykar and John Voight arXiv:1711.00125
Heuristics for the arithmetic of elliptic curves
Bjorn Poonen arXiv:1711.10112
Explicit Chabauty-Kim for the Split Cartan Modular Curve of Level 13
Jennifer S. Balakrishnan, Netan Dogra, J. Steffen Müller, Jan Tuitman, Jan Vonk arXiv:1711.05846
Gonality of dynatomic curves and strong uniform boundedness of preperiodic points
John R. Doyle, Bjorn Poonen arXiv:1711.04233
Explicit Coleman integration for curves
Jennifer S. Balakrishnan and Jan Tuitman arXiv:1710.01673
Using zeta functions to factor polynomials over finite fields
Bjorn Poonen arXiv:1710.00970
Maps between curves and arithmetic obstructions
Andrew V. Sutherland and José Felipe Voloch arXiv:1709.05734v1
Sylvester’s Problem and Mock Heegner Points
Samit Dasgupta, John Voight arXiv:1707.05874
Rigorous computation of the endomorphism ring of a Jacobian
Edgar Costa, Nicolas Mascot, Jeroen Sijsling, John Voight arXiv:1705.09248
Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties
Jennifer S. Balakrishnan, Netan Dogra arXiv:1705.00401
Statistics of K-groups modulo p for the ring of integers of a varying quadratic number field
Bruce W. Jordan, Zev Klagsbrun, Bjorn Poonen, Christopher Skinner, Yevgeny Zaytman arXiv:1703.00108
Rational Points on Varieties
Bjorn Poonen
Fast Jacobian arithmetic for hyperelliptic curves of genus 3
Andrew V. Sutherland arXiv:1607.08602
Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture
Rafael von Känel, Benjamin Matschke arXiv:1605.06079
The analytic class number formula for 1-dimensional affine schemes
Bruce W. Jordan, Bjorn Poonen arXiv:1604.04564
Sato-Tate Distributions
Andrew V. Sutherland arXiv:1604.01256
A heuristic for boundedness of ranks of elliptic curves
Jennifer Park, Bjorn Poonen, John Voight, Melanie Matchett Wood. arXiv:1602.01431
Abelian varieties isogenous to a power of an elliptic curve
Bruce W. Jordan, Allan G. Keeton, Bjorn Poonen, Eric M. Rains, Nicholas Shepherd-Barron, John T. Tate arXiv:1602.06237