Publications
Listed in reverse chronological order.
44. Efficiency in Symmetric 2x2 games
with Ellie Gunderson, to appear in Involve, 34 pages.
43. The landscape of L-functions: degree 3 and conductor 1
with David W. Farmer, Sally Koutsoliotas, and Stefan Lemurell, Contemporary Mathematics, 796, 2024, 26 pages
42. Variedades abelianas, una introducción
with Marc Hindry and Marusia Rebolledo, Publicaciones Matemáticas del Uruguay, 18, 2023, 287–365
41. Hypergeometric Motives
with Fernando Rodriguez Villegas, Notices of the AMS, June/July 2022, 914-929.
40. Abelian surfaces with fixed 3-torsion
with Frank Calegari and Shiva Chidambaram, ANTS 14, The Open Book Series 4 (2020), 91-108.
39. Quadratic relations between Feynman integrals
with David Broadhurst, Loops and Legs in Quantum Field Theory 2018.
38. Mixed degree number field computations
with John Jones, Ramanujan Journal, 47 (2018), no. 1, 47-66.
37. L-series and Feynman integrals
with David Broadhurst, Matrix Annals 2017, 401-403.
35. The explicit formula and a motivic splitting
Matrix Annals 2017, 429-433.
34. PGL2(Fl) number fields with rational companion forms
International Journal of Number Theory 14 (2018), no. 3, 825-845.
33. Newforms with rational coefficients
The Ramanujan Journal 46 (2018), no. 3, 835-862.
32. Artin L-functions of small conductor
with John Jones. Research in Number Theory 3 (2017), Article 16, 33 pages.
31. A three-parameter clan of Hurwitz-Belyi maps
Pub. Math. de Besançon, Algèbre et Théorie des Nombres, 2018, 69-83.
30. Hurwitz-Belyi maps
Pub. Math. de Besançon, Algèbre et Théorie des Nombres, 2018, 25-67.
29. Hurwitz number fields
New York Journal of Mathematics 23 (2017) 227-272.
28. Serre weights and wild ramification in two-dimensional Galois representations
with Lassina Dembélé and Fred Diamond. Forum of Mathematics, Sigma 4 (2016).
27. Hurwitz monodromy and full number fields
with Akshay Venkatesh. Algebra and Number Theory 9 (2015) no. 3, 511-545.
26. Division polynomials with Galois group SU3(3).2 = G2(2)
Advances in the theory of numbers, 169-206, Fields Inst. Commun., 77, 2015.
25. Polynomials with prescribed bad primes
International Journal of Number Theory 11 (2015), no. 4, 1115-1148.
24. Lightly ramified number fields with Galois group S.M12.A
Journal de Théorie des Nombres de Bordeaux 28 (2016), no. 2, 435-560.
23. A database of number fields
with John Jones. London Journal of Mathematics and Computation, 17 (1) (2014) 595-618.
22. The tame-wild principle for discriminant relations for number fields
with John Jones. Algebra and Number Theory 8 (2014), no. 3, 609-645.
21. Nonsolvable polynomials with field discriminant 5A
International Journal of Number Theory 7 (2011), 289-322.
19. Number fields ramified at one prime
with John Jones. ANTS VIII, Springer Lecture Notes in Computer Sciences 5011 (2008), 226-239.
18. Intersection numbers of Heegner divisors on Shimura curves
with Kevin Keating. Pure and Applied Mathematics Quarterly, Vol. 4 Num. 4 (2008), 1165-1204.
17. Wild partitions and number theory
Journal of Integer Sequences, Vol. 10, (2007), Article 07.6.6, 34 pages.
16. Nash equilibria in Cauchy-random zero-sum and coordination matrix games
International Journal of Game Theory, 34 (2006), 167-184.
15. Galois number fields with small root discriminant
with John Jones. Journal of Number Theory, 122 (2007), 379-407.
14. Fractalized cyclotomic polynomials
Proceedings of the American Mathematical Society, 135 (2007), 1959-1967.
13. A database of local fields
Journal of Symbolic Computation, Volume 41 no. 1 (2006), 80-97.
12. Pure Nash equilibria of coordination matrix games
Economics Letters, Volume 89, Issue 1 (2005), 7-11.
11. Number fields with discriminant ±2a3b and Galois group An or Sn
with Gunter Malle. London Mathematical Society Journal of Computation and Mathematics, 8, (2005). 80-101.
10. Nonic 3-adic Fields
with John Jones. ANTS-VI, Springer Lecture Notes in Computer Science, 3076 (2004), 293-308.
9. An ABC construction of number fields
CNTA-VII, CRM Proceedings and Lecture Notes, 36, (2004), 237-267.
8. Frobenius classes in alternating groups
Rocky Mountain Journal of Mathematics, Volume 34, Number 4, Winter 2004, 1483--1496. Includes accompanying Mathematica file.
7. Septic fields with discriminant ±2a3b
with John Jones. Mathematics of Computation, 72 (2003), 1975-1985.
6. Discriminants of some Painlevé polynomials
Number Theory for the Millennium III, AK Peters, (2002) 205-221. Includes accompanying Mathematica file.
5. Density of cubic field discriminants
Mathematics of Computation, 70 (2001), 1699-1705.
4. Sextic number fields with discriminant −j2a3b
with John Jones. CNTA-V, CRM Proceedings and Lecture Notes, 19, (1999) 141-172.
3. Timing analysis of targeted Hunter searches
with John Jones. ANTS-III, Springer Lecture Notes in Computer Science, 1423, (1998), 412-423.
2. Twin sextic algebras
Rocky Mountain Journal of Mathematics, 28, (1998) 341-368.
1. Composita of sextic fields, theory and examples
Communications in Algebra, 24, (1996) 3311-3334.
Thesis: Shimura curves analogous to X0(N)
97 pages.