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 theo...

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Bibliographic Details
Published in:Annales mathématiques du Québec 2023-10, Vol.47 (2), p.403-442
Main Author: Chen, Shih-Yu
Format: Article
Language:English
Subjects:
Algebra
Analysis
Homology
Mathematics
Mathematics and Statistics
Number Theory
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Summary: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 GL 3 × GL 2 .
ISSN:2195-4755
2195-4763
DOI:10.1007/s40316-021-00169-3