Discoveries / number-theory

Zhi-Wei Sun's Conjecture 3.4 on a Truncated Legendre-Symbol Determinant

Zhi-Wei Sun conjectured a closed evaluation of a truncated Legendre-symbol determinant. For every prime $p \equiv 3 \pmod 4$ it equals $\lfloor (p-2)/3 \rfloor^2 x$, proved by reducing to inverse data for Chapman's full Legendre-symbol matrix and evaluating that with Vsemirnov's factorization and a Schur-Pfaffian resolvent identity.