with its connections to the Birch and Swinnerton-Dyer conjecture, see [@Skinner1] and [@Skinner]. Provided one has both the analytic and algebraic machinery, the Iwasawa main conjecture can be formulated for higher dimensional modular forms and groups, for example [@Wan]

The algebraic theory of half-integral weight modular forms, both classical and metaplectic, has long been inchoate due to the difficulties present in developing the ‘Galois side’. Recent work by M. Weissmann in [@Weissmann] has made progress in this regard by developing $L$-groups for metaplectic covers, the length and methods of which further underline the difficulties present here. The analytic theory is substantial however, and in this paper we give the analytic construction of the $p$-adic $L$-function for Siegel modular forms of half-integral weight and any degree $n$. In [@Mercuri] we gave a similar construction when $n = 1$; in that case the $p$-adic $L$-function was already known to exist by the Shimura correspondence, this is not so for general $n>1$.

The proof found here is adapted from the method of A. Panchishkin found in Chapters 2 and 3 of [@Panchishkin], which proves the existence of the analytic $p$-adic $L$-function for Siegel modular forms of integral weight and even degree $n$. This 