## Number Theory - Anup Dixit (Queen's University)

### Tuesday, February 26th, 2019

**Time:** 1:00-2:00 p.m. **Place:** Jeffery Hall 422

**Speaker:** Anup Dixit (Queen's University)

**Title:** An extremal property of general Dirichlet series.

**Abstract:** A general Dirichlet series is given by $F(s)=\sum_{n=1}^{\infty} a_n/ \lambda_n^s$. Our goal is to realize $F(s)$ as a unique boundary element for a class of functions. In other words, is there a naturally occurring class of functions, for which $F(s)$ is the unique solution to an extremal problem? In this talk, we undertake this question and as a consequence show that an $L$-function satisfying a certain growth condition is uniquely determined by its degree, conductor, and its residue at $s=1$.