## Number Theory Seminar

### Tuesday, January 8th, 2019

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

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

**Title:** Large values on the 1-line for a family of L-functions.

**Abstract:** A classical problem in analytic number theory is to understand the values of L-functions in the critical strip. It is well-known that $|\zeta(1+it)|$ takes arbitrarily large values when $t$ runs through the real numbers. In 2006, Granville and Soundarajan conjectured that there exists arbitrarily large $t$ such that $|\zeta(1+it)|$ satisfies a certain lower bound. We discuss recent progress towards this conjecture and also generalize it to a family of L-functions. This is joint work with K. Mahatab.