Part III of the Legendre-interval series: ker L' is the pairwise-sum set of the roots of the sextic u·A(u)+1 (hexad, S6 ≅ Sp4(F2)); Witt–Artin–Schreier sheaves give W' = −q^7 for 5-cycles unconditionally and reduce X = q^6 + q^5 to class counts and Brown invariants. Paper, code, exact data.
reproducible-research hexadecimal finite-fields number-theory quadratic-forms characteristic-2 witt-vectors exponential-sums function-fields gauss-sums prime-polynomials supersingular-curves artin-schreier-curves legendre-intervals linearised-polynomials symplectic-group sp4f2 l-polynomials
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Updated
Oct 11, 2026 - Python