Part IV of "Prime polynomials in Legendre intervals over F_{2^k}[t]": hexad formula and trace parity for Z/4 Gauss sums; the sign law is proved in all 11 Frobenius classes (v2: classes 3 2 1 and 6); X = q^6 + q^5 now depends only on the class counts. Paper, Python code, data for q = 8, 32, 128. DOI 10.5281/zenodo.23308682
python latex hexadecimal finite-fields number-theory moment-methods quadratic-forms computational-number-theory analytic-number-theory even-characteristic mathematics-research witt-vectors function-fields gauss-sums prime-polynomials legendre-intervals brown-invariant arf-invariant kloosterman-sums sp4-f2
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Oct 12, 2026 - Python