$p$-adic $L$-functions for ${\rm GSp}(4)\times {\rm GL}(2)$ II

TL;DR

This paper constructs four-variable $p$-adic $L$-functions for cuspidal Hida families on ${\rm GSp}(4)\times{\rm GL}(2)$, providing a complete interpolation formula and advancing the understanding of $p$-adic $L$-functions in automorphic forms.

Contribution

It introduces a new construction of four-variable $p$-adic $L$-functions for specific automorphic families and establishes a comprehensive interpolation formula.

Findings

Constructed four-variable $p$-adic $L$-functions for ${\rm GSp}(4)\times{\rm GL}(2)$.

Proved a complete interpolation formula for these $p$-adic $L$-functions.

Computed archimedean zeta integrals using partial interpolation and existing $p$-adic $L$-functions.

Abstract

We construct four-variable $p$-adic $L$-functions for cuspidal Hida families on ${\rm GSp}(4)\times{\rm GL}(2)$ and prove a complete interpolation formula. The archimedean zeta integrals are computed by using a partial interpolation formula for the four-variable $p$-adic $L$-functions and some previously constructed $p$-adic $L$-functions.