Jacobi sums of order $2l^2$

TL;DR

This paper investigates congruences for Jacobi sums of order 2l^2 over finite fields and expresses these sums using Dickson-Hurwitz sums, advancing understanding of their algebraic properties.

Contribution

It derives new congruences for Jacobi sums of order 2l^2 and expresses these sums explicitly in terms of Dickson-Hurwitz sums, providing novel formulas.

Findings

Derived congruences for Jacobi sums of order 2l^2

Expressed Jacobi sums in terms of Dickson-Hurwitz sums

Enhanced understanding of algebraic properties of these sums

Abstract

The aim of this paper is to deal with congruences for Jacobi sums of order $2l^{2}$ over a finite field $\mathbb{F}_{q}, q=p^{r}$, $p^{r}\equiv 1\ (mod \ 2l^{2})$, where $l>3$ and $p$ are primes. Further, we also calculate Jacobi sums $J_{2l^{2}}(1,n)$ of order $2l^{2}$ in terms of Dickson-Hurwitz sums.