Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture
Rafael von Känel, Benjamin Matschke arXiv:1605.06079
Quadrilaterals inscribed in convex curves
Benjamin Matschke arXiv:1801.01945
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
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:2007.01749
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
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
Computing Classical Modular Forms for Arbitrary Congruence Subgroups
Eran Assaf arXiv:2002.07212
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
Dual linear programming bounds for sphere packing via modular forms
Henry Cohn, Nicholas Triantafillou arXiv:1909.04772
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
Restriction of Scalars, the Chabauty-Coleman Method, and P^1 \ {0,1,\infty}
Nicholas Triantafillou
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
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
On basic and Bass quaternion orders
Sara Chari, Daniel Smertnig, John Voight arXiv:1903.00560
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, Research in Number Theory, 4:23, 2018
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
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, Graduate Studies in Mathematics 186, Amer. Math. Soc., 2017
Bjorn Poonen
Fast Jacobian arithmetic for hyperelliptic curves of genus 3
Andrew V. Sutherland arXiv:1607.08602
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