Gauss factorials of polynomials over finite fields

TL;DR

This paper introduces the concept of Gauss factorials for polynomials over finite fields, establishing an initial framework for their study as analogues to classical Gauss factorials of integers.

Contribution

It pioneers the investigation of Gauss factorials in the context of polynomials over finite fields, extending classical number theory concepts to function fields.

Findings

Defined Gauss factorials for polynomials over finite fields

Established foundational properties and analogies with integer factorials

Laid groundwork for further research in polynomial factorials over finite fields

Abstract

In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.