On new identities of Jacobi sums and related cyclotomic matrices

TL;DR

This paper explores new identities of Jacobi sums and their relation to cyclotomic matrices, confirming a conjecture by Z.-W. Sun and strengthening existing results.

Contribution

It introduces novel identities of Jacobi sums and links these to cyclotomic matrices, providing proof for a conjecture and advancing the understanding of their arithmetic properties.

Findings

Confirmed Z.-W. Sun's 2019 conjecture

Established new identities of Jacobi sums

Connected Jacobi sums to cyclotomic matrices

Abstract

In this paper, using some arithmetic properties of Jacobi sums, we investigate some products involving Jacobi sums and reveal the connections between these products and certain cyclotomic matrices. In particular, as an application of our main results, we confirm a conjecture posed by Z.-W. Sun in 2019, and obtain a stronger result.