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Period relations for Rankin–Selberg convolutions for ${\mathrm {GL}}(n)\times {\mathrm {GL}}(n-1)$

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  11 September 2024

Jian-Shu Li ,
Dongwen Liu  and
Binyong Sun
Jian-Shu Li
Affiliation:
Institute for Advanced Study in Mathematics, Zhejiang University, Hangzhou 310058, China jianshu@zju.edu.cn
Dongwen Liu
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China maliu@zju.edu.cn
Binyong Sun
Affiliation:
Institute for Advanced Study in Mathematics and New Cornerstone Science Laboratory, Zhejiang University, Hangzhou 310058, China sunbinyong@zju.edu.cn
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Abstract

We formulate and prove the archimedean period relations for Rankin–Selberg convolutions for ${\mathrm {GL}}(n)\times {\mathrm {GL}}(n-1)$. As a consequence, we prove the period relations for critical values of the Rankin–Selberg L-functions for ${\mathrm {GL}}(n)\times {\mathrm {GL}}(n-1)$ over arbitrary number fields.

Keywords

cohomological representationRankin–Selberg convolutioncritical valueL-functionperiod relation

MSC classification

Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F75: Cohomology of arithmetic groups 22E45: Representations of Lie and linear algebraic groups over real fields

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Type
Research Article
Information
Compositio Mathematica , Volume 160 , Issue 8 , August 2024 , pp. 1871 - 1915
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Copyright
© 2024 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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