The shifted fourth moment of modular form L -functions in the weight aspect
Abstract
Abstract We prove a reciprocity-type formula for the fourth moment of L -functions associated with holomorphic primitive cusp forms of level one and large weight which relates it to the eighth moment of the Riemann zeta function and the dual weighted fourth moments of automorphic L -functions (both holomorphic and Maass). The main objective of the article is to study the structure of the main term for possible generalization of the method to higher moments.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Advanced Mathematical Identities
Publication details
- Journal / source
- Canadian Journal of Mathematics
- Publisher
- Canadian Mathematical Society
- Pages
- 1–54
- Publication date
- 5 January 2026
- Language
- EN