## Number Theory Seminar

### Tuesday, September 11th, 2018

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

**Speaker:** M. Ram Murty (Queen's University)

**Title:** Some reflections on Hasse's inequality (Part 1)

**Abstract:** In 1935, Hasse proved the Riemann hypothesis for zeta functions attached to elliptic curves (mod p) which was originally conjectured in the 1922 doctoral thesis of Emil Artin. There are two papers, one by Davenport in 1931 and another by Mordell in 1933 that discuss elementary approaches to this conjecture that give suprisingly non-trivial estimates. Both papers make use of a clever averaging argument that later appears in Bombieri's proof of Weil's theorem on the Riemann hypothesis for curves. We will give a motivated (and somewhat leisurely) discourse on these developments.