Simons Collaborationon Arithmetic Geometry, Number Theory, and Computation

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

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

Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Eran Assaf arXiv:2002.07212

Visualizing modular forms

David Lowry-Duda arXiv:2002.05234

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 is small

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

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

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

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

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

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

On the paramodularity of typical abelian surfaces

Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, John Voight, David S. Yuen arXiv:1805.10873

A Database of Belyi Maps

Michael Musty, Sam Schiavone, Jeroen Sijsling, John Voight arXiv:1805.07751

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