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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.

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number-theoryJun 21, 2026Significance 10/100Registry: unreviewed

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

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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.

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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.

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