Endoscopic congruences modulo adjoint $L$-values for $\mathrm{GSp}(4)$

Abstract

We establish the existence of congruences between a fixed endoscopic cuspidal automorphic representation $\Pi$ of $\mathrm{GSp}(4)$ of square-free conductor and stable cuspidal automorphic representations of the same level and weight modulo certain prime factors of the value at $1$ of the adjoint $L$-function of $\Pi$ normalized by a suitable period.

References in corpus (4)

• Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over ${\mathbb{Z}}_p$ for representations with p-small weights
• On higher regulators of Siegel threefolds II: the connection to the special value
• Arthur's multiplicity formula for GSp${}_4$ and restriction to Sp${}_4$
• On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\mathrm{GSp}}_4$

Cited by in corpus (1)

• On Petersson norms of generic cusp forms and special values of adjoint $L$-functions for ${\mathrm{GSp}}_4$