On exponential sums over multiplicative subgroups in arbitrary finite fields

Abstract:

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