Non-Archimedean L-Functions: Of Siegel and Hilbert Modular Forms
Non-Archimedean L-Functions: Of Siegel and Hilbert Modular Forms
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非阿基米德 L 函数：西格尔和希尔伯特模形式
DOI：
10.1007/978-3-662-21541-8
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发表时间：
1991
影响因子：
4.9
通讯作者：
A. A. Panchishkin
中科院分区：
文献类型：
--
作者：
A. A. Panchishkin
这本书的主要主题是自守形式的zeta函数的算法。更准确地说，它着眼于这些函数的特殊值的p-adic性质。对于黎曼zeta函数这可以追溯到经典的库默同余伯努利数和他们的p-adic解析继续标准zeta函数的西格尔和模形式和卷积的希尔伯特模形式。这本书是给专家在代表性理论，功能分析和代数几何。连同新的结果，它提供了相当多的背景资料，对p-adic措施，梅林变换，西格尔和希尔伯特模块化形式，Hecke运营商对他们的作用，和欧拉产品。
The main subject of the book is the arithmetic of zeta functions of automorphic forms. More precisely, it looks at p-adic properties of the special values of these functions. For the Riemann-zeta function this goes back to the classical Kummer congruences for Bernoulli numbers and their p-adic analytic continuation of the standard zeta functions of Siegel and modular forms and of the convolutions of Hilbert modular forms. The book is addressed to specialists in representation theory, functional analysis and algebraic geometry. Together with new results, it provides considerable background information on p-adic measures, their Mellin transforms, Siegel and Hilbert modular forms, Hecke operators acting on them, and Euler products.