## Number Theory - Siddhi Pathak (Queen's University)

### Tuesday, February 12th, 2019

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

**Speaker:** Siddhi Pathak (Queen's University)

**Title:** Distribution of special values of $L$-series attached to Erdos functions.

**Abstract:** Inspired by Dirichlet's theorem that $L(1,\chi) \neq 0$ for a non-principal Dirichlet character $\chi$, S. Chowla initiated the study of non-vanishing of $L(1,f)$ for a rational valued, $q$-periodic arithmetical function $f$. In this context, Erdos conjectured that $L(1,f) \neq 0$ when $f$ takes values in $\{ -1, 1\}$. This conjecture remains open in the case $q \equiv 1 \bmod 4$ or when $q > 2 \phi(q) + 1$. In this talk, we discuss a density theoretic approach towards this conjecture and the distribution of these values.