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

TL;DR

This paper constructs p-adic L-functions that interpolate critical values of degree eight L-functions for GSp(4)×GL(2), linking automorphic forms and number theory in a novel way.

Contribution

It introduces a new method to construct p-adic L-functions for GSp(4)×GL(2) using p-ordinary Siegel and modular forms, expanding the scope of p-adic L-function theory.

Findings

Successfully interpolates critical L-values for GSp(4)×GL(2)

Connects automorphic representations with p-adic L-functions

Provides tools for future research in automorphic forms

Abstract

We construct $p$-adic $L$-functions interpolating the critical values of the degree eight $L$-functions of ${\rm GSp}(4)\times {\rm GL}(2)$ for cuspidal automorphic representations generated by $p$-ordinary Siegel modular forms of genus two and $p$-ordinary modular forms.