# Higher Hida theory and p-adic L-functions for GSp(4)

## TL;DR

This paper develops a new p-adic interpolation method using higher Hida theory to construct p-adic L-functions for automorphic forms on GSp(4), advancing the understanding of special values of these L-functions.

## Contribution

It introduces higher Hida theory for GSp(4), enabling p-adic interpolation of periods of non-holomorphic automorphic forms and constructing associated p-adic L-functions.

## Key findings

- Constructed p-adic L-functions for GSp(4) degree 4 and GSp(4) x GL(2) degree 8 L-functions.
- Extended the scope of p-adic interpolation to non-holomorphic automorphic forms.
- Provided new tools for studying special values of automorphic L-functions.

## Abstract

We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent cohomology of Siegel threefolds in positive degrees. We apply this new method to construct p-adic L-functions associated to the degree 4 (spin) L-function of automorphic representations of GSp(4), and the degree 8 L-function of GSp(4) x GL(2).