Davenport-Hasse's Theorem for Polynomial Gauss Sums over Finite Fields

TL;DR

This paper extends Davenport-Hasse's theorem to polynomial Gauss sums over finite fields, generalizing previous results and providing new insights into their algebraic properties.

Contribution

It introduces an analogue of Davenport-Hasse's theorem specifically for polynomial Gauss sums over finite fields, broadening the theoretical framework.

Findings

Established an analogue of Davenport-Hasse's theorem for polynomial Gauss sums.

Generalized Hayes's previous results to a broader class of sums.

Enhanced understanding of algebraic structures of polynomial Gauss sums.

Abstract

In this paper, we study the polynomial Gauss sums over finite fields, and present an analogue of Davenport-Hasse's theorem for the entire polynomial Gauss sums, which is a generalization of the previous result obtained by Hayes.