Proves explicit determinant formulas and a uniform congruence modulo p for Legendre symbol matrices, resolving parts of Sun's conjectures 4.8(i) and 4.10(i).
evil determinant
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.NT 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
For every prime p ≡ 3 mod 4, the truncated Legendre-symbol determinant evaluates to floor((p-2)/3)^2 x via reduction to Chapman's matrix inverse using Vsemirnov factorization and Schur-Pfaffian identity.
citing papers explorer
-
Two determinant evaluations in Sun's conjectures involving Legendre symbols
Proves explicit determinant formulas and a uniform congruence modulo p for Legendre symbol matrices, resolving parts of Sun's conjectures 4.8(i) and 4.10(i).
-
A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant
For every prime p ≡ 3 mod 4, the truncated Legendre-symbol determinant evaluates to floor((p-2)/3)^2 x via reduction to Chapman's matrix inverse using Vsemirnov factorization and Schur-Pfaffian identity.