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

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.

Final version, accepted in Compositio Math

Cited by in corpus (13)

• Euler systems for GSp(4)
• Higher Hida theory and p-adic L-functions for GSp(4)
• Anticyclotomic Euler systems for unitary groups
• P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)
• Functoriality of motivic lifts of the canonical construction
• A class number formula for Picard modular surfaces
• Algebraic cycles and functorial lifts from $G_2$ to ${\mathrm{PGSp}}_6$
• Mahler's measure and elliptic curves with potential complex multiplication
• Spinor Euler factors for GSp(4) in the subregular case
• Endoscopic congruences modulo adjoint $L$-values for $\mathrm{GSp}(4)$
• Regular poles for spinor $L$-series attached to split Bessel models of $\mathrm{GSp}(4)$
• The Ranking-Selberg integral on $\mathbf{GSp}(2)$ for square free levels
• Algebraic cycles and residues of degree eight $L$-functions of $\mathrm{GSp}(4)\times \mathrm{GL}(2)$