## Number Theory - Neha Prabhu (Queen's University)

### Tuesday, September 25th, 2018

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

**Speaker:** Neha Prabhu (Queen's University)

**Title:** The error term in the Sato-Tate theorem of Birch.

**Abstract:** In 1968, Birch proved a vertical analogue of the Sato-Tate conjecture for elliptic curves showing the asymptotic behaviour of $a_E(p)$, a quantity associated to an elliptic curve $E$ mod p. An error term for this result was obtained by Banks and Shparlinski in 2009 using the results of Katz and Neiderreiter. In this talk, we shall see that this error term can also be obtained in an elementary fashion using ideas in Birch's paper. This is joint work with Ram Murty.