Frank Thorne

University of South Carolina
Department of Mathematics
400-G LeConte College
1523 Greene Street
Columbia, SC 29201
thorne [at] math [dot] sc [dot] edu


Teaching

Math 788, The Geometry of Numbers, Spring 2014.

Math 580, Elementary Number Theory, Fall 2013.

Math 142, Calculus II, Fall 2013.

Math 788p, Topics in Algebraic Number Theory, Spring 2013.

Reading seminars: Complex analysis, Mondays at 10:00 am; Algebraic geometry, Wednesdays at 9:30 am.

Math 531, Foundations of Geometry, Fall 2012.

Math 141, Calculus I, Fall 2012.

Math 574, Discrete Math, Spring 2012.

Math 141, Calculus I, Fall 2011.

Math 782, Analytic Number Theory, Fall 2011.


I work in number theory. Some of my particular interests:

Graduate Students: Richard Oh and Daniel Kamenetsky.

Curriculum vitae.

My talk at the Joint Meetings: 1 + 2 + 3 + 4 + ...

Dartmouth: 1 + 2 + 3 + 4 + ...

Seminars at the University of South Carolina:

Number Theory Seminar, Spring 2013

South Carolina Algebraic Geometry, Commutative Algebra, Number Theory, Fall 2013

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.

3. Bubbles of congruent primes.
Mathematical Proceedings of the Cambridge Philosophical Society, to appear.

4. An uncertainty principle for function fields.
Journal of Number Theory 131 (2011), 1363-1389.

5. Maier matrices beyond Z.
Proceedings of the Integers Conference 2007.

6. Analytic properties of Shintani zeta functions.
Proceedings of the RIMS Symposium on automorphic forms, automorphic representations, and related topics (Kyoto, 2010).

7. The secondary term in the counting function for cubic fields, with Takashi Taniguchi.
Duke Mathematical Journal, to appear.

8. Shintani's zeta function is not a finite sum of Euler products.
Proceedings of the American Mathematical Society, to appear.

9. Orbital L-functions for the space of binary cubic forms, with Takashi Taniguchi.
Canadian Journal of Mathematics, to appear.

10. Four perspectives on secondary terms in the Davenport-Heilbronn theorems.
Integers Volume 12B, Proceedings of the Integers Conference 2011.

11. An error estimate for counting S_3-sextic number fields, with Takashi Taniguchi.
International Journal of Number Theory, to appear.

Supplementary files: CountS3.java, sextic-compare.gp, and an old note with some supplementary numerical data.

More supplementary files: css.gp, css-5.gp, and ParseBelabas.java.

12. Book review of Opera de Cribro and An introduction to sieve methods and their applications.
Bulletin of the American Mathematical Society, to appear.

13. On the existence of large degree Galois representations for fields of small discriminant, with Jeremy Rouse.
Submitted.

14. Dirichlet series associated to cubic fields with given quadratic resolvent,with Henri Cohen.
Michigan Math Journal, to appear.

See below [11] for source code; also: a short list of cubic fields generated by Karim Belabas's program.

15. Dirichlet series associated to quartic fields with given resolvent, with Henri Cohen.
Submitted.

Appendix: Complete proof of Theorem 5.1, whose proof was only sketched in the paper.

16. Zeros of L-functions outside the critical strip, with Andrew Booker.
Submitted.

17. Identities for field extensions generalizing the Ohno-Nakagawa relations, with Henri Cohen and Simon Rubinstein-Salzedo.
Submitted.

Supplementary file: nakagawa.gp.

Several more in preparation.

Upcoming/Recent Professional Activities:

Palmetto Number Theory Series, Clemson, December 7-8, 2013.

Pro p-groups and arithmetic, Besançon, December 16-20, 2013.

Automorphic Forms and Arithmetic, Gottingen, February 10-14, 2014.

University of Bonn, March 4-14, 2014.

Zürich Number Theory Days, March 7-8, 2014.

Arizona Winter School, Tucson, March 15-19, 2014.

Southeast Regional Meeting on Numbers, Wofford College, April 19-20, 2014.

Ursinus College, early May.

Bateman and Halberstam, University of Illinois, June 5-7, 2014.

Counting Arithmetic Objects, Montreal, June 23-July 4, 2014.

Richard Oh's thesis defense, July 8, 2014.

Emerging Leaders and Evolving Frontiers in Analytic Number Theory, Bonn, July 14-18, 2014.

Gangnam Style, August 13-21, 2014.

Emory University, August 27, 2014.

Workshop on Counting Arithmetic Objects, Montreal, November 10-14, 2014.

Analysis, Spectra, and Number Theory, Princeton, December 15-19, 2014.