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p‐adic L‐functions on metaplectic groups
Journal of the London Mathematical Society ( IF 1.2 ) Pub Date : 2020-04-30 , DOI: 10.1112/jlms.12318
Salvatore Mercuri 1
Affiliation  

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.

中文翻译:

代谢组的p-adic L功能

关于解析-代数二分法,半积分权重的Siegel模块化形式的理论是不正确的;分析理论很强,而代数则落后。在本文中,我们利用这一点来确定岩泽主要猜想的分析方面所需的基本对象: p -adic 大号 通过对复数进行插值获得的函数 大号 -以特殊值起作用。这是通过Rankin-Selberg方法和非亚纯Siegel Eisenstein级数的显式傅里叶展开实现的。的建设 p 在这种情况下的稳定也具有独立的意义。
更新日期:2020-04-30
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