Frank Thorne

NSF Postdoctoral Fellow
Stanford University
Department of Mathematics
382-X Sloan Hall
Stanford, CA 94305
thorne [at] math [dot] sc [dot] edu


Additive Combinatorics, Spring 2011.
This website is out of date, and not actively maintained. Please visit me at the University of South Carolina. Speak in our number theory seminar while you're at it!

My research interests include various aspects of analytic and algebraic number theory. Recently I have become very interested in Shintani zeta functions and their applications to counting number fields.

Curriculum vitae. (a little bit out of date, for now)

Informal seminar in analytic number theory.

Publications and Preprints:

1. Bounded gaps between products of primes with applications to elliptic curves and ideal class groups, International Mathematics Research Notices (2008), 41 pp.

2. Irregularities in the distributions of primes in function fields, Journal of Number Theory 128 (2008), 1784-1794, accepted for publication.

3. Bubbles of congruent primes, under revision.

4. An uncertainty principle for function fields, Journal of Number Theory, accepted for publication.

5. Maier matrices beyond Z (survey paper), Proceedings of the Integers Conference 2007, accepted for publication.

6. Analytic properties of Shintani zeta functions, Proceedings of the RIMS Symposium on automorphic forms, automorphic representations, and related topics.

7. The secondary term in the counting function for cubic fields (with Takashi Taniguchi), submitted.

In preparation, drafts available on request.

8. Orbital L-functions for the space of binary cubic forms (with Takashi Taniguchi), draft version in progress.

9. An improved version of the effective Chebotarev density theorem, in progress.

10. (with K. Soundararajan) On the existence of large degree representations for fields of small discriminant, in progress.

11. Prime and almost prime discriminants of cubic fields, (dead).

12. (with K. Soundararajan) Zeros of Dirichlet series outside the critical strip, in progress.

Dead letter office.

Recent or Upcoming Professional Activities.

University of Georgia, January 19, 2011.

Emory University, January 20, 2011.

The Number Theory of Partitions, January 21-23, 2011.

University of South Carolina, January 24-28, 2011.

Arithmetic Statistics, MSRI, Berkeley, 2011. Introductory workshop, January 31-February 4, 2011.

McGill University, March 17, 2011 (cancelled due to jury duty).

Analytic aspects of L-functions and applications to number theory, Calgary, May 29-June 3, 2011.

L-functions and number theory, Meeting of the Canadian Mathematical Society, Edmonton, June 3-5, 2011.

The Cohen-Lenstra heuristics for class groups, AIM, Palo Alto, CA, June 13-17, 2011.

Mathematical Research Community on Multiplicative Functions, Snowbird, UT, June 26-July 2011 (co-organizer along with a couple of pretentious characters)

Previous talks.

Other Stuff

To be added (?)