Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

TL;DR

This paper constructs an anticyclotomic $p$-adic $L$-function interpolating square roots of central twisted spinor $L$-values for quadratic base changes of genus 2 Siegel cusp forms, assuming the B"ocherer conjecture.

Contribution

It introduces a new construction of a $p$-adic $L$-function related to genus 2 Siegel cusp forms under specific conjectural assumptions.

Findings

Construction of the $p$-adic $L$-function interpolates central $L$-values.

Relates B"ocherer conjecture to $p$-adic $L$-functions.

Provides a framework for further arithmetic applications.

Abstract

We construct the anticyclotomic $p$-adic $L$-function that interpolates a square root of central values of twisted spinor $L$-functions of a quadratic base change of a Siegel cusp form of genus $2$ with respect to a paramodular group of square-free level, assuming the B\"ocherer conjecture for the central $L$-values with anticyclotomic twists.