Non-vanishing of central values of L-functions with angular restrictions
Number Theory
2026-01-30 v1
Abstract
We study the angular restrictions for the second moment of toroidal families of -functions using the general theory of trace functions. With the mollification technique we deduce non-vanishing of a positive proportion. Our two main ingredients are classification results of Katz to determine the sheaves at play and a recent result of Fouvry, Kowalski, Michel and Sawin to bound bilinear sums of their trace functions.
Cite
@article{arxiv.2601.21642,
title = {Non-vanishing of central values of L-functions with angular restrictions},
author = {Filippo Berta and Svenja zur Verth},
journal= {arXiv preprint arXiv:2601.21642},
year = {2026}
}
Comments
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