Moments of L‐functions via a relative trace formula
Abstract
Abstract We prove an asymptotic formula for the second moment of the Rankin–Selberg central ‐values , where is a fixed cuspidal representation of that is tempered and unramified at every place, while varies over a family of automorphic representations of ordered by their (archimedean or non‐archimedean) conductors. As another application of our method, we prove existence of infinitely many cuspidal representations of such that and do not vanish simultaneously where and are cuspidal representations of that are unramified and tempered at every place and have trivial central characters.
Fields of Study & Subjects
Advanced Algebra and Geometry
Finite Group Theory Research
Analytic Number Theory Research
Publication details
- Journal / source
- Proceedings of the London Mathematical Society
- Volume
- 132
- Issue
- 4
- Publication date
- 1 April 2026
- Language
- EN