Linnik’s problem on Hecke-Maass cuspforms and effective multiplicity one theorem,

Min Lee (Bristol University)

December 30 (Mon)   2019, 13:00 ~14:15 아산이학관 526호

AbstractThe strong multiplicity one theorem implies that if two Hecke-Maass cuspforms share the same Laplacian eigenvalue and the same Hecke eigenvalues for almost all Hecke operators, then the two forms must be equal to some constant multiplication. In this talk, we change the “almost all” to “finitely many”, and consider the following two related questions:
(1) Given a set of finite Hecke operators, how large is the dimension of the joint eigenspace of the given Hecke operators and the Laplace operator?
(2) How many Hecke operators are needed to conclude that two given forms are equal?
This is a joint work with Junehyuk Jung.

Artin's primitive root conjecture for function fields without Riemann Hypothesis 

Seoyeong Kim (Queen’s University)

December 30 (Mon)   2019, 14:15~15:15 아산이학관 526호

AbstractArtin's primitive root conjecture for function fields is known by Bilharz in his thesis in 1937, which was conditional on the proof of the Riemann hypothesis for global function fields, which was proved by Weil in 1948. In this talk, we suggest a simple proof of Artin's primitive root conjecture for function fields by using the technique from the proof of the prime number theorem by Hadamard and de la Vall/'ee Poussin. This is joint work with M. Ram Murty.