Books
B1. | [PDF] | Quaternion algebras, current draft version. |
Articles
Please note that the versions that appear here may differ from the published version, as some errata have been corrected. The version here is the most updated; the arXiv versions are updated less often.
42. | [PDF] | [1602.02637] | A database of Hilbert modular forms (with Steve Donnelly). |
41. | [PDF] | [1612.09249] | Zeta functions of alternate mirror Calabi-Yau families (with with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher), submitted. |
39. | [PDF] | [1702.00092] | 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), submitted. |
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] | A heuristic for boundedness of ranks of elliptic curves (with Jennifer Park, Bjorn Poonen, and Melanie Matchett Wood), submitted. |
35. | [PDF] | [1510.04637] [Link] | On the arithmetic dimension of triangle groups (with Steve Nugent), Math. Comp. 86, no. 306, July 2017, 1979-2004. |
34. | [PDF] | [1405.6059] [Errata] [Link] | Nonvanishing of twists of L-functions attached to Hilbert modular forms (with Nathan C. Ryan and Gonzalo Tornaría), LMS J. Comput. Math. 17 (Special issue A) (2014), 330-348. |
33. | [PDF] | [1504.04642] | Fake quadrics (with Benjamin Linowitz and Matthew Stover), submitted. |
32. | [PDF] | [1504.02814] [Link] [Direct Link] | On explicit descent of marked curves and maps (with Jeroen Sijsling), Res. Number Theory 2:27 (2016), 35 pages. |
31. | [PDF] | [1209.2460] [Errata] [Link] | 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] | 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] | Discriminants and the monoid of quadratic rings, Pacific J. Math. 283 (2016), no. 2, 483-510. |
26. | [PDF] | [1010.5727] [Errata] [Link] | 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] [Errata] [Link] | Rings of low rank with a standard involution, Illinois J. Math. 55 (2011), no. 3, 1135-1154. |
24. | [PDF] | [1501.04657] | The canonical ring of a stacky curve (with David Zureick-Brown), submitted. |
23. | [PDF] | [1311.2081] [Errata] [Link] | Numerical computation 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] [Errata] [Link] | 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, Contemporary Mathematics, vol. 521, Amer. Math. Soc., Providence, RI, 2010, 21-28. |
20. | [PDF] | [0906.4374] [Errata] [Link] | 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] [Errata] [Link] | 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] | Algebraic curves uniformized by congruence subgroups of triangle groups (with Pete L. Clark), accepted to Trans. Amer. Math. Soc. |
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] | 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] | 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] | 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] [Errata] [Link] |
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] | 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. |
Tables
L-Functions and Modular Forms Database (LFMDB)
- 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)