Character sums over elements of extensions of finite fields with restricted coordinates

TL;DR

This paper establishes new bounds for character sums over finite field elements with restricted coordinates, including a finite field analogue of the Cantor set, advancing understanding of sum estimates in algebraic structures.

Contribution

It introduces novel bounds for character sums over elements with restricted coordinates in finite fields, including the Cantor set analogue, expanding the scope of sum estimates.

Findings

Derived nontrivial bounds for character sums over restricted elements

Extended sum estimates to finite field analogues of fractal sets

Provided new tools for analyzing algebraic structures with restrictions

Abstract

We obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite field analogue of the Cantor set.