# Algebra/Number Theory Seminar

## Explicit bounds on the least primitive root modulo p

Kevin McGown, CSU, Chico

Wednesday, May 8th, 2019
12:00 PM - 1:00 PM
Hylan 1106A

A classical problem in analytic number theory is to give an upper bound on the least primitive root modulo p, denoted by g(p). In the 1960s Burgess proved that (for any eps>0) one has g(p)<p^{1/4+eps} for sufficiently large p. This was a consequence of his landmark character sum inequality, and this result remains the state of the art. However, in applications, explicit estimates are often required, and there is a lot “hiding in the epsilon”. Recently, Trudgian and the speaker have given an explicit upper bound on g(p) that improves (by a small power of log factor) on what one can obtain using any existing version of the Burgess inequality. We will discuss this and other related results.

Event contact: dinesh dot thakur at rochester dot edu