irreducible-polynomials

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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
TeX

Ruqing1963 / oppermann-function-fields

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Oppermann intervals in F_q[t]: characteristic-2 counterexamples with exact counts for d ≤ 3, an exact d = 2 formula for odd q, and a Hayes-FFT census

finite-fields computational-number-theory explicit-formula number-theory-tool short-intervals function-fields gauss-sums irreducible-polynomials oppermann-conjecture characteristic-two

Updated Oct 14, 2026
Python

Ruqing1963 / legendre-intervals-explicit-formula

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Draft (unpublished): exact explicit-formula verification of the function-field Legendre conjecture for d <= 10, fluctuations of prime counts, and a characteristic-2 anomaly.

finite-fields number-theory random-matrix-theory computer-assisted-proof exact-arithmetic explicit-formula legendre-conjecture function-fields irreducible-polynomials hayes-characters

Updated Oct 8, 2026
Python

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