Quartic Gauss sums over primes and metaplectic theta functions

Fuente: arXiv
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Hauptverfasser: David, Chantal, Dunn, Alexander, Hamieh, Alia, Lin, Hua
Format: Preprint
Veröffentlicht: 2023
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author David, Chantal
Dunn, Alexander
Hamieh, Alia
Lin, Hua
author_facet David, Chantal
Dunn, Alexander
Hamieh, Alia
Lin, Hua
contents We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares. We also conjecture asymptotics for certain moments of quartic Gauss sums over primes.
format Preprint
id arxiv_https___arxiv_org_abs_2306_11875
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Quartic Gauss sums over primes and metaplectic theta functions
David, Chantal
Dunn, Alexander
Hamieh, Alia
Lin, Hua
Number Theory
11F27, 11F30, 11L05, 11L20, 11N36
We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares. We also conjecture asymptotics for certain moments of quartic Gauss sums over primes.
title Quartic Gauss sums over primes and metaplectic theta functions
topic Number Theory
11F27, 11F30, 11L05, 11L20, 11N36
url https://arxiv.org/abs/2306.11875