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arXiv · 2601.21642

Non-vanishing of central values of L-functions with angular restrictions

Filippo Berta·Svenja zur Verth
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Abstract

We study the angular restrictions for the second moment of toroidal families of $L$-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.

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Filippo Berta, Svenja zur Verth. 2026-01-29. Non-vanishing of central values of L-functions with angular restrictions. https://arxiv.org/abs/2601.21642

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