# $p$-adic $L$-functions on metaplectic groups

## TL;DR

This paper constructs p-adic L-functions for metaplectic groups by interpolating special values of complex L-functions, using Rankin-Selberg methods and Fourier expansions of Siegel Eisenstein series, advancing the analytic side of Iwasawa theory.

## Contribution

It establishes the fundamental p-adic L-function for metaplectic groups, bridging the analytic and algebraic aspects in the context of Iwasawa main conjecture.

## Key findings

- Construction of p-adic L-functions via Fourier expansion methods
- Explicit p-stabilisation technique developed for metaplectic groups
- Advancement in the analytic theory of Siegel modular forms of half-integral weight

## Abstract

With respect to the analytic-algebraic dichotomy, the theory of Siegel modular forms of half-integral weight is lopsided; the analytic theory is strong whereas the algebraic lags behind. In this paper, we capitalise on this to establish the fundamental object needed for the analytic side of the Iwasawa main conjecture -- the $p$-adic $L$-function obtained by interpolating the complex $L$-function at special values. This is achieved through the Rankin-Selberg method and the explicit Fourier expansion of non-holomorphic Siegel Eisenstein series. The construction of the $p$-stabilisation in this setting is also of independent interest.