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Algebraicity of the central critical values of twisted triple product L-functions

Algebraicity of the central critical values of twisted triple product L-functions We study the algebraicity of the central critical values of twisted triple product L-functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in the totally unbalanced case. The algebraicity is expressed in terms of the cohomological period constructed via the theory of coherent cohomology on quaternionic Shimura varieties developed by Harris. As an application, we generalize our previous result with Cheng on Deligne’s conjecture for certain automorphic L-functions for GL3×GL2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text {GL}}_3 \times {\text {GL}}_2$$\end{document}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales mathématiques du Québec Springer Journals

Algebraicity of the central critical values of twisted triple product L-functions

Annales mathématiques du Québec , Volume 47 (2): 40 – Oct 1, 2023

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References (83)

Publisher
Springer Journals
Copyright
Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2021
ISSN
2195-4755
eISSN
2195-4763
DOI
10.1007/s40316-021-00169-3
Publisher site
See Article on Publisher Site

Abstract

We study the algebraicity of the central critical values of twisted triple product L-functions associated to motivic Hilbert cusp forms over a totally real étale cubic algebra in the totally unbalanced case. The algebraicity is expressed in terms of the cohomological period constructed via the theory of coherent cohomology on quaternionic Shimura varieties developed by Harris. As an application, we generalize our previous result with Cheng on Deligne’s conjecture for certain automorphic L-functions for GL3×GL2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\text {GL}}_3 \times {\text {GL}}_2$$\end{document}.

Journal

Annales mathématiques du QuébecSpringer Journals

Published: Oct 1, 2023

Keywords: Critical values; Triple product L-functions; Deligne’s conjecture; Primary 11F67; Secondary 11F70; 11F75

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