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

### Tuesday, October 9th, 2018

**Time:** 10:00 a.m. **Place:** Jeffery Hall 422

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

**Title:** On the Euler-Kronecker constants.

**Abstract:** In 2006, Y. Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to any number field $K$, which is a generalization of the Euler-Mascheroni constant. This constant surprisingly arises in several seemingly unrelated aspects of analytic number theory. Ihara studied this constant systematically and produced bounds on $gamma_K$ under GRH. In this talk, we prove unconditional bounds for $\gamma_K$ in some cases and discuss its connection to the Brauer-Siegel theorem.