The distribution and extreme values of Dirichlet L-functions

3:00pm, Wednesday 26th February

Abstract

The $L$-functions are fundamental objects in number theory, encoding arithmetic information about numbers, polynomials, and algebraic objects like elliptic curves. Their special values often reveal deep insights, including connections to class numbers in algebraic number fields.

This talk focuses on the distribution and extreme values of Dirichlet $L$-functions, $L(s, \chi)$, where $s$ is a complex variable and $\chi$ is a Dirichlet character $\pmod{q}$. Particular focus will be placed on the behavior of these functions within the critical strip $(1/2\leq \Re(s)\leq 1)$. The presentation will aim to  make the topic accessible to a general audience.