Uniform subconvexity and symmetry breaking reciprocity

TL;DR

This paper establishes a non-symmetric reciprocity formula linking moments of automorphic L-functions across different levels and characters, leading to uniform subconvexity bounds in level and eigenvalue aspects.

Contribution

It introduces a novel reciprocity formula that connects moments of automorphic L-functions of different levels and characters, enabling new subconvexity bounds.

Findings

Established a non-symmetric reciprocity formula.

Derived uniform subconvexity bounds in level and eigenvalue aspects.

Connected moments of automorphic L-functions across different levels.

Abstract

A non-symmetric reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q and primitive central character twisted by the l-th Hecke eigenvalue as a twisted mixed moment of automorphic L-functions of level l and trivial central character. As an application, uniform subconvexity bounds for L-functions in the level and the eigenvalue aspect are derived.