## Number Theory Seminar

### Monday, January 13th, 2020

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

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

**Title:** On Picard-type theorems involving $L$-functions.

**Abstract:** The little Picard's theorem states that any non-constant entire function takes all complex values or all complex values except one point. In a similar flavour, suppose $f$ is an entire function such that for complex values $a$ and $b$, the set of zeros of $f$ is same as the set where $f'$ takes values $a$ and $b$, then it is possible to show that $f$ is a constant function. Such results are called Picard-type theorems. In this talk, we will discuss similar questions for $L$-functions, where it is possible to prove much stronger results.