# Jacobi sums and cyclotomic numbers: A survey report

## TL;DR

This survey reviews the extensive research on Jacobi sums and cyclotomic numbers, focusing on their determination, congruences, and related Diophantine systems, highlighting current progress and unresolved issues.

## Contribution

It provides a comprehensive overview of existing results and methods for calculating Jacobi sums and cyclotomic numbers, summarizing the state of the art in this area.

## Key findings

- Summary of key results on Jacobi sums and cyclotomic numbers
- Overview of Diophantine systems used for their computation
- Current open problems and future directions

## Abstract

The determination of Jacobi sums, their congruences and cyclotomic numbers have been the object of attention for many years and there are large number of interesting results related to these in the literature. This survey aims at reviewing results concerning the diophantine systems for finding the cyclotomic numbers and coefficients of Jacobi sums and to indicate the current status of the problem.