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Ruqing1963 / legendre-function-field

Legendre's conjecture in function fields (v7): proved for q >= d-1 (Hayes-Weil), verified for every q when d <= 8, conjecture for q <= d-2. Paper, review, code, data.

python latex reproducible-research finite-fields numba number-theory galois-theory computer-assisted-proof arithmetic-geometry legendre-conjecture monodromy function-fields irreducible-polynomials prime-polynomials chebotarev-density lang-weil hayes-characters keating-rudnick

Updated Oct 6, 2026
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Ruqing1963 / legendre-intervals-part2

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Prime polynomials in Legendre intervals over F_{2^k}[t], II — exact variances via quadratic towers and supersingular Artin–Schreier curves: paper (LaTeX), verification code and data (R. Chen, 2026)

python latex reproducible-research finite-fields number-theory quadratic-forms arithmetic-geometry etale-cohomology exponential-sums function-fields prime-polynomials keating-rudnick supersingular-curves artin-schreier-curves hayes-group

Updated Oct 20, 2026
TeX

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