Delphi.science

FixedNumerator: the local step in extending a theorem on quartic Gauss sums over primes to a fixed numerator

Source: github.com/jkfarland-bot/FixedNumerator/tree/817fb1416c9d54…

Joseph S. Farland

Palomar Registrypalomar/PALOMAR-2026-11-04-000003Nov 4, 2026math.NTscore 0

Theorem 1.1 of C. David, A. Dunn, A. Hamieh and H. Lin (arXiv:2306.11875) bounds the sums of normalized quartic Gauss sums g(c) over primary primes c of Z[i] in a class modulo 4, twisted by (c/|c|)^l. The companion note extends it to g(nu, c) with any fixed numerator nu. The only new ingredient is a local identity that splits off the primes dividing nu from the coprimality conditions of the Type I Dirichlet series. This development formalizes that step from the identities of DDHL Section 3, taken as hypotheses on an abstract symbol and Gauss sum: the splitting identity g(mu, pi^k c') =…

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