Schools

Seminars

Home Schools Mathematics Seminars

FIELD
Mathematics
DATE
Dec 08 (Fri), 2023
TIME
11:30 ~ 13:00
PLACE
8101
SPEAKER
Jo, Yeongseong
HOST
Lee, Youngmin
INSTITUTE
이화여자대학교
TITLE
[GS_M_NT] Rankin-Selberg integrals and symmetric square L-factors
ABSTRACT
Automorphic L-functions are generalizations of Riemann zeta functions. Their analytic properties have profound implications in dynamical systems, including, but not limited to, the prime number theorem. A problem of recurring interest, with wide-ranging applications, is to relate the special value of L-function with period of integrals. In this context, an answer to the fundamental question boils down to understanding poles and zeros of a family of certain "Rankin-Selberg" type integrals that represent various L-factors. We will review some earlier results on exterior and symmetric square L-factors. The proof involves the Bernstein-Zelevinsky derivatives and exceptional/regular poles, building upon the seminal work of Cogdell and Piatetski-Shapiro. If time permits, we will also discuss the strategy for generalizing the results from GL(2) to higher rank groups, as well as the Rankin-Selberg method for classical groups.
FILE
446041700112848088_1.pdf