# On some determinants with Legendre symbol entries

@article{Sun2019OnSD,
title={On some determinants with Legendre symbol entries},
author={Zhi-Wei Sun},
journal={Finite Fields Their Appl.},
year={2019},
volume={56},
pages={285-307}
}
• Zhi-Wei Sun
• Published 13 August 2013
• Mathematics
• Finite Fields Their Appl.
25 Citations
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A remark on Zoloterav's theorem
Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where
A Remark on Zoloterav's Theorem
Let n ≥ 3 be an odd integer. For any integer a prime to n, define the permutation γ a,n of {1,. .. , (n − 1)/2} by γ a,n (x) = n − {ax} n if {ax} n ≥ (n + 1)/2, {ax} n if {ax} n ≤ (n − 1)/2, where
On R. Chapman's "evil determinant": case p=1 (mod 4)
For p=1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the matrix C with C(i,j)=LegendreSymbol(j-i,p), i,j=0,...,(p-1)/2.
Advanced Number Theory
When a person thinks of algebra, they typically think of a process used to solve polynomial equations. Modern Number theory has evolved through several stages in the past two millennia. Notions of
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Am. Math. Mon.
• 2005
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A classical introduction to modern number theory
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Graduate texts in mathematics
• 1982
This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curve.
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We study and evaluate determinants of various matrices built up from the Legendre symbol defined modulo a prime p. MSC class: 11C20