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On higher regulators of Siegel threefolds II: the connection to the special value

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms $K$-theory in number theory

Published online by Cambridge University Press:  27 March 2017

Francesco Lemma
Francesco Lemma*
Affiliation:
Institut mathématique de Jussieu-Paris Rive Gauche, UMR 7586, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France email francesco.lemma@imj-prg.fr
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Abstract

We establish a connection between motivic cohomology classes over the Siegel threefold and non-critical special values of the degree-four $L$-function of some cuspidal automorphic representations of $\text{GSp}(4)$. Our computation relies on our previous work [On higher regulators of Siegel threefolds I: the vanishing on the boundary, Asian J. Math. 19 (2015), 83–120] and on an integral representation of the $L$-function due to Piatetski-Shapiro.

Keywords

Beilinson conjectureSiegel threefoldspinor L-function

MSC classification

Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Secondary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols 19F27: Étale cohomology, higher regulators, zeta and $L$-functions
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 5 , May 2017 , pp. 889 - 946
Copyright
© The Author 2017 

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