L-Functions in Analytic Number Theory
Analytic number theory focuses on arithmetic questions through the lens of L-functions. These generating series encode arithmetic information and have connections with a host of other mathematical fields, such as algebraic number theory, harmonic analysis, Diophantine approximation, probability, representation theory, and computational number theory. The main focuses of this CRG include moments of L-functions and automorphic forms, explicit results in analytic number theory, and comparative prime number theory.
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Xiannan Li
The behavior of quadratic twists of modular L-functions at the critical point is related both to coefficients of half integer weight modular forms and data on elliptic curves. Here we describe a proof of an asymptotic for the second moment of this...
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Shashank Chorge
We compute extreme values of the Riemann Zeta function at the critical points of the zeta function in the critical strip. i.e. the points where ζ′(s)=0 and Rs1. We show that the values taken by the zeta function at these points are very similar to...
Scientific, Seminar
PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Chung Hang (Kevin) Kwan
In the past century, the studies of moments of L-functions have been important in number theory and are well-motivated by a variety of arithmetic applications. This talk will begin with two problems in elementary number theory, followed by a survey...