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On higher regulators of Siegel threefolds II: the connection to the special value
Part of
Francesco Lemma
Journal:

Compositio Mathematica / Volume 153 / Issue 5 / May 2017

Published online by Cambridge University Press:

27 March 2017, pp. 889-946

Print publication:

May 2017
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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.