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

TL;DR

This paper links motivic cohomology classes on Siegel threefolds to special values of degree four L-functions of GSp(4) automorphic representations, advancing understanding of their arithmetic significance.

Contribution

It establishes a new connection between motivic cohomology and special L-values for Siegel threefolds, building on prior work and integral representations.

Findings

Proves a relation between motivic cohomology classes and L-values.

Utilizes integral representations to compute these special values.

Extends previous results to a broader class of automorphic forms.

Abstract

We establish a connection between motivic cohomology classes over the Siegel threefold and special values of the degree four $L$-function of some cuspidal automorphic representations of $\mathrm{GSp}(4)$. Our computation relies on our previous work [Le15] and on an integral representation of the $L$-function due to Piatetski-Shapiro.