On the cyclotomic field Q(e2πi/p) and Zhi-Wei Sun's conjecture on det M

2024/01/11 by Li-Yuan Wang, Hai-Liang Wu · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research

paper · pdf · doi:10.1016/j.ffa.2024.102533

Abstract

In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of p-th cyclotomic field and the finite field \mathbbF_p, we confirm this conjecture.

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• On a determinant involving linear combinations of Legendre symbols
• Evaluation of a determinant involving Legendre symbols

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