Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

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.