Publications

Listed in reverse chronological order. 

 

39. Quadratic relations between Feynman integrals

with David Broadhurst, to appear in Loops and Legs in Quantum Field Theory 2018.

PDF
 

38. Mixed degree number field computations

with John Jones, to appear in The Ramanujan Journal

pdf
 

37.  L-series and Feynman integrals

with David Broadhurst, to appear in Matrix Annals

PDF
 

36.  Hypergeometric supercongruences

with Fernando Rodriguez Villegas, to appear in Matrix Annals

PDF
 

35. The explicit formula and a motivic splitting

to appear in Matrix Annals

PDF
 

34. PGL2(Fl) number fields with rational companion forms

          International Journal of Number Theory 14 (2018), no. 3, 825-845.

PDF
 

33. Newforms with rational coefficients

The Ramanujan Journal 46 (2018), no. 3, 835-862.

PDF
 

32. Artin L-functions of small conductor

with John Jones. Research in Number Theory 3 (2017), Article 16, 33 pages.

PDF
 

31. A three-parameter clan of Hurwitz-Belyi maps

Pub. Math. de Besançon, Algèbre et Théorie des Nombres, 2018, 69-83.

PDF
MMA
 

30. Hurwitz-Belyi maps

Pub. Math. de Besançon, Algèbre et Théorie des Nombres, 2018, 25-67.

PDF
MMA
 

29.  Hurwitz number fields

New York Journal of Mathematics 23 (2017) 227-272.

PDF
MMA
 

28. Serre weights and wild ramification in two-dimensional Galois representations

with Lassina Dembélé and Fred Diamond. Forum of Mathematics, Sigma 4 (2016).

PDF
 

27. Hurwitz monodromy and full number fields

with Akshay Venkatesh. Algebra and Number Theory 9 (2015) no. 3, 511-545.

PDF
 

26. Division polynomials with Galois group SU3(3).2 = G2(2)

           Advances in the theory of numbers, 169-206, Fields Inst. Commun., 77, 2015.

PDF
MMA
 

25. Polynomials with prescribed bad primes

International Journal of Number Theory 11 (2015), no. 4, 1115-1148.

PDF
 

24. Lightly ramified number fields with Galois group S.M12.A

           Journal de Théorie des Nombres de Bordeaux 28 (2016), no. 2, 435-560.

PDF
 

23. A database of number fields

with John Jones. London Journal of Mathematics and Computation, 17 (1) (2014) 595-618.

PDF
 

22. The tame-wild principle for discriminant relations for number fields

with John Jones. Algebra and Number Theory 8 (2014), no. 3, 609-645. 

PDF
 

21. Nonsolvable polynomials with field discriminant 5A

          International Journal of Number Theory 7 (2011), 289-322.

PDF
 

20. Octic 2-adic fields

with John Jones. Journal of Number Theory 128 (2008), 1410-1429.

PDF
 

19. Number fields ramified at one prime

with John Jones. ANTS VIII, Springer Lecture Notes in Computer Sciences 5011 (2008), 226-239.

PDF
 

18. Intersection numbers of Heegner divisors on Shimura curves

with Kevin Keating. Pure and Applied Mathematics Quarterly, Vol. 4 Num. 4 (2008), 1165-1204.

PDF
 

17. Wild partitions and number theory

Journal of Integer Sequences, Vol. 10, (2007), Article 07.6.6, 34 pages.

PDF
 

16. Nash equilibria in Cauchy-random zero-sum and coordination matrix games

International Journal of Game Theory, 34 (2006), 167-184.

PDF
 

15. Galois number fields with small root discriminant

with  John Jones. Journal of Number Theory, 122 (2007), 379-407. 

PDF
 

14. Fractalized cyclotomic polynomials

Proceedings of the American Mathematical Society, 135 (2007), 1959-1967.

PDF
 

13. A database of local fields

Journal of Symbolic Computation, Volume 41 no. 1 (2006), 80-97.

PDF
 

12. Pure Nash equilibria of coordination matrix games

Economics Letters, Volume 89, Issue 1 (2005), 7-11. 

PDF
 

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.

PDF
 

10. Nonic 3-adic Fields

with John Jones. ANTS-VI, Springer Lecture Notes in Computer Science, 3076 (2004), 293-308.

PDF
 

9. An ABC construction of number fields

CNTA-VII, CRM Proceedings and Lecture Notes, 36, (2004), 237-267. 

PDF
 

8. Frobenius classes in alternating groups

Rocky Mountain Journal of Mathematics, Volume 34, Number 4, Winter 2004, 1483--1496. Includes accompanying Mathematica file. 

PDF
MMA
 

7. Septic fields with discriminant ±2a3b

          with John Jones. Mathematics of Computation, 72 (2003), 1975-1985.

PDF
 

6. Discriminants of some Painlevé polynomials

Number Theory for the Millennium III, AK Peters, (2002) 205-221. Includes accompanying Mathematica file.

PDF
MMA
 

5. Density of cubic field discriminants

Mathematics of Computation, 70 (2001), 1699-1705. 

DVI
 

4. Sextic number fields with discriminant −j2a3b

          with John Jones. CNTA-V, CRM Proceedings and Lecture Notes, 19, (1999) 141-172.

PDF
 

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.

PDF