On determinants involving (\fracj²-k²p) and (\fracjkp)

2024/08/26 by Deyi Chen, Zhi-Wei Sun, Chen, Deyi +1
Mathematics · Physics and Astronomy · #11A15 #11C20 #15A15 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.14401

openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime and let (\frac⋅p) be the Legendre symbol. In this paper, we study the determinant det[(\fracj²-k²p)+(\fracjkp)w]_{δ≤ j,k≤ (p-1)/2} with δ∈\0,1\. For example, we prove that the determinant does not depend on w if p≡3\pmod4 and δ=0.

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