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On a determinant involving linear combinations of Legendre symbols
- Publication Year :
- 2024
-
Abstract
- In this paper, we prove a conjecture of the second author by evaluating the determinant $$\det\left[x+\left(\frac{i-j}p\right)+\left(\frac ip\right)y+\left(\frac jp\right)z+\left(\frac{ij}p\right)w\right]_{0\le i,j\le(p-3)/2}$$ for any odd prime $p$, where $(\frac{\cdot}p)$ denotes the Legendre symbol. In particular, the determinant is equal to $x$ when $p\equiv 3\pmod4$.<br />Comment: 16 pages. Make the main result more general
- Subjects :
- Mathematics - Number Theory
11A15, 11C20, 15A15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.07034
- Document Type :
- Working Paper