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arXiv · 2306.11875

Quartic Gauss sums over primes and metaplectic theta functions

Chantal David·Alexander Dunn·Alia Hamieh·Hua Lin
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Abstract

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.

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Chantal David, Alexander Dunn, Alia Hamieh, Hua Lin. 2023-06-20. Quartic Gauss sums over primes and metaplectic theta functions. https://arxiv.org/abs/2306.11875

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