From the 2 of 5 linked papers with an AI index.
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Non-vanishing for quartic Hecke -functions and ranks of elliptic curves
Cruz Castillo, Alexandre de Faveri, Alexander Dunn
The paper proves that a positive proportion of quartic Hecke L‑functions attached to quartic residue symbols over Gaussian integers do not vanish at the central point, and uses thi…
Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg
Alexandre de Faveri, Alexander Dunn, Jeffrey Hoffstein
The paper proves that cubic and quartic large sieve families are not perfectly orthogonal, showing the obstruction comes from bias in Gauss sums and providing analytic bounds via R…
Quartic Gauss sums over primes and metaplectic theta functions
Chantal David, Alexander Dunn, Alia Hamieh +1
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 ov…
The twisted second moment of modular half integral weight --functions
Alexander Dunn, Alexandru Zaharescu
Given a half-integral weight holomorphic Kohnen newform on , we prove an asymptotic formula for large primes with power saving error term for \begin{equation*} \si…
Bias in cubic Gauss sums: Patterson's conjecture
Alexander Dunn, Maksym RadziwiÅÅ
Let be a smooth test function with compact support in . Conditional on the Generalized Riemann Hypothesis for Hecke -functions over , we prove th…