# Complete Congruences of Jacobi sums of order 2l^2 with prime l

## TL;DR

This paper derives new congruences for Jacobi sums of order 2l^2 with odd prime l, enabling algebraic and arithmetic characterizations of these sums.

## Contribution

It establishes the first known congruences for Jacobi sums of order 2l^2, expanding the theoretical understanding of these sums.

## Key findings

- Derived explicit congruences for Jacobi sums of order 2l^2
- Provided algebraic characterizations based on these congruences
- Extended previous results to a new class of sums

## Abstract

The congruences for Jacobi sums of some lower orders has been treated by many authors in the literature. In this paper we establish the congruences for Jacobi sums of order 2l^2 with odd prime l. These congruences are useful to obtain algebraic and arithmetic characterizations for Jacobi sums of order 2l^2 .