Character Sums and Deterministic Polynomial Root Finding in Finite Fields

TL;DR

This paper introduces new bounds on character sums and leverages them to develop improved deterministic algorithms for finding polynomial roots in finite fields, enhancing computational efficiency in number theory applications.

Contribution

It provides a novel bound on double multiplicative character sums and applies it to create more efficient deterministic root-finding algorithms in finite fields.

Findings

New bound on double multiplicative character sums

Improved deterministic algorithms for polynomial root finding

Enhanced computational efficiency in finite field applications

Abstract

We obtain a new bound of certain double multiplicative character sums. We use this bound together with some other previously obtained results to obtain new algorithms for finding roots of polynomials modulo a prime $p$.