Conductor zeta function for the GL(2) universal family

2021/05/05 by Farrell Brumley, Brumley, Farrell, Didier Lesesvre +3
Mathematics · #11F41 #11F72 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2105.02068

openalex publication_date 2021/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a Weyl law with power savings for the universal families of cuspidal automorphic representations, ordered by analytic conductor, of GL₂ over ℚ, as well as for Hecke characters over any number field. The method proceeds by establishing the requisite analytic properties of the underlying conductor zeta function.

Citations

• Integral moments of L-functions

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