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p ‐adic L ‐functions on metaplectic groups
Author(s) -
Mercuri Salvatore
Publication year - 2020
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12318
Subject(s) - mathematics , holomorphic function , modular form , pure mathematics , eisenstein series , conjecture , siegel modular form , algebraic number , algebra over a field , algebraic geometry and analytic geometry , function (biology) , fourier series , mathematical analysis , differential algebraic equation , ordinary differential equation , evolutionary biology , biology , differential equation
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.