Date: Thursday, December 17, 2020.
Time: 3:30 PM.
Zoom Meeting Link: https://us02web.zoom.us/j/85923312360?pwd=aFk5R2Z1alJ6dEV0UlBHQkV2aU84dz09
Meeting ID: 859 2331 2360
Passcode: 392843
On special values of Dirichlet series with periodic coefficients
Abhishek T Bharadwaj
Chennai Mathematical Institute.
17-12-20

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Abstract

The special values of a L function are expected to have some arithmetic significance. For instance, the non-vanishing of L(1,\chi) for a non-trivial Dirichlet character \chi encodes the information of infinitude of primes in arithmetic progression. The question of non-vanishing of L(1,f) for a rational valued periodic function f was first raised by S. Chowla. In this talk, we present an overview of the conjectures and results pertaining to L(k,f) for a positive integer k and a rational valued periodic function f. We shall also describe a conditional result classifying all rational valued periodic functions f for which L(k,f) is zero. This is a joint work with Siddhi Pathak