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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.'
author:
- Salvatore Mercuri
title: '<span style="font-variant:small-caps;">$p$-adic $L$-functions on metaplectic groups</span>'
---

[ oldtitletitle title[oldtitle]{}]{} [ @oldtitletitle title[@oldtitle]{}]{}

Introduction {#intro}
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Traditionally, $p$-adic $L$-functions have dual constructions – analytic and algebraic – and it is the substance of the Iwasawa main conjecture that these two are equivalent. This conjecture can be formulated for various settings; for example, over $GL_1$, the conjecture asserts that the analytic construction – Kubota-Leopoldt’s $p$-adic interpolation of the Dirichlet $L$-function – is equivalent to Iwasawa’s algebraic $p$-adic $L$-function. The Iwasawa main conjecture for classical modular forms of integral weight is formulated over $GL_2$ and this has been a recent, active research area 