PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:Atkin and Swinnerton-Dyer Congruences
Seminar:Algebra and Number Theory Seminar
Speaker:Ling Long, Cornell and Louisiana State Universities
Abstract:
In the study of modular forms for noncongruence subgroups of SL(2,Z), despite the lack of effective Hecke operators, the coefficients of noncongruence modular forms satisfy some remarkable congruences called Atkin and Swinnerton-Dyer (ASD) congruences. They are often viewed as p-adic Hecke operators and are of fundamental importance to the study of noncongruence modular forms. More generally, it has been observed that special sequences arising from combinatorics, arithmetic, or differential equations also satisfy ASD type congruences. Some of them turned out to be p-adic analogues of Ramanujan type formula for 1 over Pi. In this talk, we will introduce Atkin and Swinnerton-Dyer congruences, survey some recent developments, and discuss their applications and connections to other areas.

Room Reservation Information

Room Number:MB106
Date:02 / 14 / 2013
Time:11:15am - 12:05pm