Articles
Please note that the versions that appear here may differ from the published version, as the errata have been corrected. The version here is the most up-to-date; the arXiv versions are updated less often.
78. | [PDF] | The value of mathematical storytelling: our perspective on giving talks (with Bianca Viray), submitted. | |
70. | [PDF] | [2203.08593] | Stickelberger's discriminant theorem for algebras (with Asher Auel and Owen Biesel), accepted to Amer. Math. Monthly. |
66. | [PDF] | [2203.08593] [Code] |
Triangular modular curves of small genus (with Juanita Duque-Rosero), accepted to Res. Number Theory. |
65. | [PDF] | [2203.06405] [Link] |
Definite orthogonal modular forms: computations, excursions, and discoveries (with Eran Assaf, Dan Fretwell, Colin Ingalls, Adam Logan, and Spencer Secord), Res. Number Theory. 8:70 (2022), 38 pages. |
64. | [PDF] | [2111.07504] | Computing Euclidean Belyi maps (with Matthew Radosevich), submitted. |
63. | [PDF] | [2106.11141] [Link] |
Appendix A: Jacobians of arbitrary modular curves (with Jeremy Rouse, Andrew V. Sutherland, and David Zureick-Brown), appendix to Jeremy Rouse, Andrew V. Sutherland, and David Zureick-Brown, ell-adic images of Galois for elliptic curves over Q, Forum Math. Sigma 10 (2022), e62. |
62. | [PDF] | [Link] | The L-Functions and Modular Forms Database (with John Cremona, John Jones, and Andrew V. Sutherland), Notices Amer. Math. Soc. 68 (2021), no. 9, 1520-1522. |
61. | [PDF] | [2004.14022] [Link] |
A canonical form for positive definite matrices (with Mathieu Dutour Sikirić, Anna Haensch, and Wessel P.J. van Woerden), Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), ed. Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020, 179-195. |
60. | [PDF] | [1908.00421] [Link] |
A Prym variety with everywhere good reduction over Q(√61) (with Nicolas Mascot and Jeroen Sijsling), Arithmetic Geometry, Number Theory, and Computation, eds. Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, and John Voight, Simons Symp., Springer, Cham, 2021, 559-581. |
59. | [PDF] | [1906.07877] [Link] [Errata] |
Counting elliptic curves with an isogeny of degree three (with Maggie Pizzo and Carl Pomerance), Proc. Amer. Math. Soc. Ser. B 7 (2020), 28-42. |
58. | [PDF] | [2002.04717] [Link] [Errata] |
Computing classical modular forms (with Alex J. Best, Jonathan Bober, Andrew R. Booker, Edgar Costa, John Cremona, Maarten Derickx, David Lowry-Duda, Min Lee, David Roe, and Andrew V. Sutherland), Arithmetic Geometry, Number Theory, and Computation, eds. Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, and John Voight, Simons Symp., Springer, Cham, 2021, 131-213. |
57. | [PDF] | [2005.06669] [Link] [Code] |
On a probabilistic local-global principle for torsion on elliptic curves (with John Cullinan and Meagan Kenney), J. Théorie Nombres Bordeaux 34 (2022), no. 1, 41-90. |
56. | [PDF] | [1907.12103] [Link] |
On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (with John Cremona, Lassina Dembélé, Ariel Pacetti, and Ciaran Schembri), Arithmetic Geometry, Number Theory, and Computation, eds. Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, and John Voight, Simons Symp., Springer, Cham, 2021, 343-363. |
55. | [PDF] | [1906.07384] [Code] [Link] |
Special hypergeometric motives and their L-functions: Asai recognition (with Lassina Dembélé, Alexei Panchishkin, and Wadim Zudilin), accepted to Exp. Math. |
54. | [PDF] | [2203.07787] | On Galois inertial types of elliptic curves over Q_{l} (with Lassina Dembélé and Nuno Freitas), preprint. |
53. | [PDF] | [Link] | Alternate mirror families and hypergeometric motives (with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher), 2017 MATRIX Annals, eds. David R. Wood, Jan de Gier, Cheryl E. Praeger, and Terence Tao, MATRIX Book Series, vol. 2, Springer Nature, Switzerland, 2019, 441-448. |
52. | [PDF] | [Link] | Triangular modular curves, 2017 MATRIX Annals, eds. David R. Wood, Jan de Gier, Cheryl E. Praeger, and Terence Tao, MATRIX Book Series, vol. 2, Springer Nature, Switzerland, 2019, 481-483. |
51. | [PDF] | [1711.00125] [Link] |
The Belyi degree of a curve is computable (with Ariyan Javanpeykar), Arithmetic geometry: computation and applications, Contemp. Math., vol. 722, Amer. Math. Soc., Providence, RI, 2019, 43-57. |
50. | [PDF] | [1910.00449] [Code] | On unit signatures and narrow class groups of odd degree abelian number fields (with Ben Breen and Ila Varma; appendix with Ben Breen, Noam Elkies, and Ila Varma), accepted to Trans. Amer. Math. Soc. |
49. | [PDF] | [1906.02803] [Link] |
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms (with Edgar Costa and Davide Lombardo), Res. Number Theory 7:46 (2021), 14 pages. |
48. | [PDF] | [1903.00560] [Link] | On basic and Bass quaternion orders (with Sara Chari and Daniel Smertnig), Proc. Amer. Math. Soc. Ser. B 8 (2021), 11-26. |
47. | [PDF] | [1707.05874] [Link] [Errata] |
Sylvester's problem and mock Heegner points (with Samit Dasgupta), Proc. Amer. Math. Soc. 146 (2018), no. 8, 3257-3273. |
46. | [PDF] | [1903.10662] [Code] [Link] [Errata] |
Definite orders with locally free cancellation (with Daniel Smertnig), Trans. Lond. Math. Soc. 6 (2019), no. 1, 53-86. |
45. | [PDF] | [1705.09248] [Code] [Link] [Errata] |
Rigorous computation of the endomorphism ring of a Jacobian (with Edgar Costa, Nicolas Mascot, and Jeroen Sijsling), Math. Comp. 88 (2019), 1303-1339. |
44. | [PDF] | [1805.07751] [Link] |
A database of Belyi maps (with Michael Musty, Sam Schiavone, and Jeroen Sijsling), Proceedings of the Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII), eds. Renate Scheidler and Jonathan Sorenson, Open Book Series 2, Mathematical Sciences Publishers, Berkeley, 2019, 375-392. |
43. | [PDF] | [1810.06254] [Code] [Link] |
Hypergeometric decomposition of symmetric K3 quartic pencils (with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher), Res. Math. Sci. 7:7 (2020), 81 pages. |
42. | [PDF] | [1602.02637] [Link] |
A database of Hilbert modular forms (with Steve Donnelly), Arithmetic Geometry, Number Theory, and Computation, eds. Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, and John Voight, Simons Symp., Springer, Cham, 2021, 365-373. |
41. | [PDF] | [1612.09249] [Link] |
Zeta functions of alternate mirror Calabi-Yau families (with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher), Israel J. Math. 228 (2018), 665-705. |
40. | Sato-Tate groups and automorphy for atypical abelian surfaces (with Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, and Dan Yasaki), forthcoming. | ||
39. | [PDF] | [1702.00092] [Link] [Errata] |
The 2-Selmer group of a number field and heuristics for narrow class groups and signature ranks of units (with David S. Dummit; appendix with David S. Dummit and Richard Foote), Proc. London Math. Soc. 117 (2018), 682-726. |
38. | [PDF] | [1805.10873] [Code] [Link] [Errata] |
On the paramodularity of typical abelian surfaces (with Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaría, and David S. Yuen), Algebra & Number Theory 13 (2019), no. 5, 1145-1195. |
37. | [PDF] | [1602.03715] [Link] [Errata] |
A database of genus 2 curves over the rational numbers (with Andrew R. Booker, Jeroen Sijsling, Andrew V. Sutherland, and Dan Yasaki), LMS J. Comput. Math. 19 (Special Issue A) (2016), 235-254. |
36. | [PDF] | [1602.01431] [Link] | A heuristic for boundedness of ranks of elliptic curves (with Jennifer Park, Bjorn Poonen, and Melanie Matchett Wood), J. European Math. Soc. 21 (2019), no. 9, 2859-2903. |
35. | [PDF] | [1510.04637] [Code] [Link] [Errata] |
On the arithmetic dimension of triangle groups (with Steve Nugent), Math. Comp. 86 (2017), no. 306, 1979-2004. |
34. | [PDF] | [1405.6059] [Link] [Errata] |
Nonvanishing of twists of L-functions attached to Hilbert modular forms (with Nathan C. Ryan and Gonzalo Tornaría), LMS J. Comput. Math. 19 (Issue A) (2014), 330-348. |
33. | [PDF] | [1504.04642] [Code] [Link] |
Commensurability classes of fake quadrics (with Benjamin Linowitz and Matthew Stover), Selecta Math. (New Ser.) 25:48 (2019), 39 pages. |
32. | [PDF] | [1504.02814] [Link] [Errata] |
On explicit descent of marked curves and maps (with Jeroen Sijsling), Res. Number Theory 2:27 (2016), 35 pages. |
31. | [PDF] | [1209.2460] [Link] [Errata] |
Lattice methods for algebraic modular forms on classical groups (with Matthew Greenberg), Computations with modular forms, eds. Gebhard Boeckle and Gabor Wiese, Contrib. Math. Comput. Sci., vol. 6, Springer, Berlin, 2014, 147-179. |
30. | [PDF] | [1408.2001] [Link] [Errata] |
Small isospectral and nonisometric orbifolds of dimension 2 and 3 (with Benjamin Linowitz), Math. Z. 281 (2015), no. 1, 523-569. |
29. | [PDF] | [1205.0045] [Link] [Errata] |
Computing power series expansions of modular forms (with John Willis), Computations with modular forms, eds. Gebhard Boeckle and Gabor Wiese, Contrib. Math. Comput. Sci., vol. 6, Springer, Berlin, 2014, 331-361. |
28. | [PDF] | [1311.2529] [Link] [Errata] |
On computing Belyi maps (with Jeroen Sijsling), Publ. Math. Besançon: Algèbre Théorie Nr. 2014/1, Presses Univ. Franche-Comté, Besançon, 73-131. |
27. | [PDF] | [1504.05228] [Link] [Errata] |
Discriminants and the monoid of quadratic rings, Pacific J. Math. 283 (2016), no. 2, 483-510. |
26. | [PDF] | [1010.5727] [Link] [Errata] |
Explicit methods for Hilbert modular forms (with Lassina Dembélé), Elliptic curves, Hilbert modular forms and Galois deformations, Birkhauser, Basel, 2013, 135-198. |
25. | [PDF] | [1003.3512] [Link] [Errata] |
Rings of low rank with a standard involution, Illinois J. Math. 55 (2011), no. 3, 1135-1154. |
24. | [PDF] | [1501.04657] [Link] [Errata] |
The canonical ring of a stacky curve (with David Zureick-Brown), Mem. Amer. Math. Soc. 277 (2022), no. 1362. |
23. | [PDF] | [1311.2081] [Link] [Errata] |
Numerical calculation of three-point covers of the projective line (with Michael Klug, Michael Musty, and Sam Schiavone), LMS J. Comput. Math. 17 (2014), no. 1, 379-430. |
22. | [PDF] | [1004.5340] [Link] [Errata] |
Computing automorphic forms on Shimura curves over fields with arbitrary class number, Algorithmic number theory (ANTS IX, Nancy, France, 2010), eds. Guillaume Hanrot, Francois Morain, and Emmanuel Thomé, Lecture Notes in Comp. Sci., vol. 6197, Springer, Berlin, 2010, 357-371. |
21. | [PDF] | [0907.2060] | Nondegenerate curves of low genus over small finite fields (with Wouter Castryck), Arithmetic, Geometry, Cryptography and Coding Theory 2009, Contemp. Math., vol. 521, Amer. Math. Soc., Providence, RI, 2010, 21-28. |
20. | [PDF] | [0906.4374] [Link] [Errata] |
Nonsolvable number fields ramified only at 3 and 5 (with Lassina Dembélé and Matthew Greenberg), Compositio Math. 147 (2011), no. 3, 716-734. |
19. | [PDF] | [0904.4310] [Link] [Errata] |
Characterizing quaternion rings over an arbitrary base, J. Reine Angew. Math. 657 (2011), 113-134. |
18. | [PDF] | [0904.3908] [Link] |
Computing systems of Hecke eigenvalues associated to Hilbert modular forms (with Matthew Greenberg), Math. Comp. 80 (2011), 1071-1092. |
17. | [PDF] | [1506.01371] [Link] [Errata] |
Algebraic curves uniformized by congruence subgroups of triangle groups (with Pete L. Clark), Trans. Amer. Math. Soc. 371 (2019), no. 1, 33-82. |
16. | [PDF] | [1112.4881] [Link] [Errata] |
Computing zeta functions of nondegenerate hypersurfaces with few monomials (with Steven Sperber), LMS J. Comp. Math. 16 (2013), 9-44. |
15. | [PDF] | [1004.0994] [Link] [Errata] |
Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms, Quadratic and higher degree forms, eds. K. Alladi, M. Bhargava, D. Savitt, and P.H. Tiep, Developments in Math., vol. 31, Springer, New York, 2013, 255-298. |
14. | [PDF] | [0808.3833] [Link] [Tables] [Corrigendum] [Errata] |
Algorithmic enumeration of ideal classes for quaternion orders (with Markus Kirschmer), SIAM J. Comput. (SICOMP) 39 (2010), no. 5, 1714-1747; Corrigendum: Algorithmic enumeration of ideal classes for quaternion orders, SIAM J. Comput. (SICOMP) 41 (2012), no. 3, 714. |
13. | [PDF] | [0806.0306] [Link] [Errata] |
The Gauss higher relative class number problem, Ann. Sci. Math. Québec 32 (2008), no. 2, 221-232. |
12. | [PDF] | [0802.0911] [Link] [Tables] [Errata] |
Shimura curves of genus at most two, Math. Comp. 78 (2009), 1155-1172. |
11. | [PDF] | [0802.0196] [Link] [Demo] [Errata] |
Computing fundamental domains for Fuchsian groups, J. Théorie Nombres Bordeaux 21 (2009), no. 2, 467-489. |
10. | [PDF] | [0802.0420] [Link] [Errata] |
On nondegeneracy of curves (with Wouter Castryck), Algebra & Number Theory 3 (2009), no. 3, 255-281. |
9. | [PDF] | [0802.0194] [Link] [Tables] [Errata] |
Enumeration of totally real number fields of bounded root discriminant, Algorithmic number theory (ANTS VIII, Banff, 2008), eds. Alfred van der Poorten and Andreas Stein, Lecture Notes in Comp. Sci., vol. 5011, Springer, Berlin, 2008, 268-281. |
8. | [PDF] | Shimura curve computations, Arithmetic Geometry, Clay Math. Proc., vol. 8, Amer. Math. Soc., Providence, 2009, 103-113. | |
7. | [PDF] | [Errata] | Heegner points and Sylvester's conjecture (with Samit Dasgupta), Arithmetic Geometry, Clay Math. Proc., vol. 8, Amer. Math. Soc., Providence, 2009, 91-102. |
6. | [PDF] | [0410266] [Link] [Errata] |
Quadratic forms that represent almost the same primes, Math. Comp. 76 (2007), 1589-1617. |
5. | [PDF] | [Link] [Errata] |
Computing CM points on Shimura curves arising from cocompact arithmetic triangle groups, Algorithmic number theory (ANTS VII, Berlin, 2006), eds. Florian Hess, Sebastian Pauli, Michael Pohst, Lecture Notes in Comp. Sci., vol. 4076, Springer, Berlin, 2006, 406-420. |
4. | [Link] | Arithmetic Fuchsian groups and Shimura curves, Quaternion algebras (with David Kohel), Associative orders (with Nicole Sutherland), Handbook of Magma functions, eds. John Cannon and Wieb Bosma, Sydney, ed. 2.14, 2007. | |
3. | [PDF] | [Link] | Curves over finite fields with many points: an introduction, Computational aspects of algebraic curves, ed. Tanush Shaska, Lecture Notes Series on Computing, vol. 13, World Scientific, Hackensack, NJ, 2005, 124-144. |
2. | [PDF] | Quadratic forms and quaternion algebras: Algorithms and arithmetic, Ph.D. thesis, University of California, Berkeley, 2005. | |
1. | [PDF] | On the nonexistence of odd perfect numbers, MASS Selecta: Teaching and learning advanced undergraduate mathematics, eds. Svetlana Katok, Alexei Sossinsky, and Serge Tabachnikov, American Mathematical Society, Providence, RI, 2003, 293-300. |
Books
- Quaternion algebras, home page.
Tables
L-Functions and Modular Forms Database (LMFDB)
- Hilbert modular forms
- Totally real number fields of fixed degree and bounded root discriminant
- Shimura curves of genus at most two
- Definite Eichler orders with class number at most two
Notes
- [PDF] Perfect numbers: An elementary introduction
- [PDF] Introduction to stacks
- [PDF] Toric surfaces and continued fractions
- [Link] Oberwolfach seminar on Explicit Algebraic Number Theory
- [PDF] Aspects of complex multiplication (notes from Zagier)
- [PDF] Introduction to group schemes (notes from Schoof)
- [Link] Rational and integral points on higher dimensional varieties (notes from AIM)
- [PDF] Algebraic geometry (notes from Hartshorne)