Work

Moments of symmetric square L$L$‐functions on GL(3)${\rm GL}(3)$

Year: 2025

Type: article

Abstract: We give an asymptotic formula with power saving error term for the twisted first moment of symmetric square ‐functions on in the level aspect. As applications, we obtain nonvanishing results as well as lower bounds of the expected order of magnitude for all even moments, supporting the random matrix model for a unitary ensemble. Besides the Kuznetsov formula, the ingredients include detailed local computations at ramified places, including root numbers and orthonormalization of oldforms and Eisenstein series.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70033

Authors: Valentin Blomer, Félicien Comtat

Institution: University of Bonn

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,700

Funders: Deutsche Forschungsgemeinschaft, European Research Council