{"id":"palomar/PALOMAR-2026-11-04-000003","url":"https://github.com/jkfarland-bot/FixedNumerator/tree/817fb1416c9d54140c6bbdd9b2d08f37b481d934","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-04-000003-v1.json","repo":"https://github.com/jkfarland-bot/FixedNumerator","tags":["math.NT","msc:11L05","msc:11R18","msc:11N13","msc:68V20"],"score":0,"title":"FixedNumerator: the local step in extending a theorem on quartic Gauss sums over primes to a fixed numerator","trust":"high","domain":"math.NT","source":"palomar","authors":["Joseph S. Farland"],"reviews":0,"subject":"math.NT","summary":"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') =…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-04","reactions":{},"formalized":true,"formalizes":[{"title":"Quartic Gauss sums over primes with a fixed numerator","identifier":"https://doi.org/10.5281/zenodo.23882882","relationship":"formalizes"}]}