Torus periods of automorphic functions and the meromorphic continuation of related Dirichlet Series

2010/08/05 by Andre Reznikov, André Reznikov, Reznikov, Andre
Mathematics · #11M41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11M41

paper · pdf · doi:10.48550/arxiv.1008.0995

21 p. Corrections for the polar divisor are made, proofs for cusp forms and for real quadratic fields are added. New title

openalex publication_date 2010/08/05 · arxiv created 2011/12/30 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider modular functions (i.e., the Eisenstein series and Hecke-Maass forms) for the group PSL(2,Z). We fix a quadratic number field E. This gives rise to twisted (by a Hecke character of the field E) periods of a modular function along the torus corresponding to E. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.

Related

• Automorphicity and Mean-Periodicity
• On certain period relations for cusp forms on GL_n
• Dirichlet series constructed from periods of automorphic forms
• Twisted periods of modular forms
• Harmonic Maass forms and periods