Non-vanishing of central values of L-functions with angular restrictions
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.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint