# On exponential sums over multiplicative subgroups in arbitrary finite fields

## Affiliation:

Sydney University

## Date:

Wed, 18/04/2018 - 3:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

We present a range of new sum-product type estimates in finite fields $\mathbb F_q$, where $q$ is a prime power. We then outline how these estimates lead to explicit bounds on exponential sums over multiplicative subgroups in $\mathbb F_q$. In particular, these bounds improve and complement results of Bourgain and Glibichuk (2011) and Zhelezov (2017).