Modular Forms: Basics and Beyond
Modular Forms: Basics and Beyond
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模块化形式：基础知识及其他
DOI：
10.1007/978-1-4614-2125-2
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
G. Shimura
中科院分区：
文献类型：
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作者：
G. Shimura
这是一本关于模形式的高级书籍。虽然有许多关于模形式的书出版，但它们都是在初级水平上写的，从已经知道基础知识的读者的角度来看并不那么有趣。这本书提供了一些新的东西，可以满足这样一个读者的愿望。然而，我们陈述了关于一个变量的经典模形式的每一个定义和每一个基本事实。其中一个主要的新特点，这本书是理论的模块化形式的半整重量，另一个是讨论θ函数和爱森斯坦系列的全纯和nonholomorphic类型。因此，本书的提出是为了让读者能够系统地学习这些理论。最后，我们集中讨论了以下两个问题：（1）半整权形式与整权形式之间的对应关系。(II)与整权或半整权的模形式有关的各种狄利克雷级数的算术性。
This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes:(I) The correspondence between the forms of half-integral weight and those of integral weight.(II) The arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight.