## Number Theory Seminar

### Tuesday, September 17th, 2019

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 319

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

**Title:** On Euler-Kronecker constants and the prime number theorem.

**Abstract:** As a generalization of the Euler-Mascheroni constant $\gamma$, Y. Ihara defined the the Euler-Kronecker constant $\gamma_K$ attached to a number field $K/\mathbb{Q}$. Ihara conjectured that for a cyclotomic fields $K$, $\gamma_K >0$. This initiated the study of the bounds on $\gamma_K$ for cyclotomic fields. In this talk, we describe an application of these bounds to the error term in the prime number theorem for certain arithmetic progressions. This is joint work with Prof. M. Ram Murty.