Modular forms: basics and beyond
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 …
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- Full title :Modular forms : basics and beyond / Goro Shimura.
Summary
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. Goro Shimura is currently a professor emeritus of mathematics at Princeton University.
Read More ↓Edition Statements
- Publication Date:2012
Publication Statements
- Publisher(s):Springer
- Place of Publication:New York
- Language:eng
- Publication Date:2012
The Physical Object
- Description:x, 175 pages ; : 24 cm
Edition Identifiers
- ISBN:9781461421245, 1461421241, 146142125X, 9781461421252
- DOI:10.1007/978-1-4614-2125-2
- oclc:ocn756595307
- LC Classification:QA243
- Dewey Decimal:512.7/3
Table of Contents
Ch. I. Preliminaries -- Ch. II. Theta functions and factors -- Ch. III. The rationality and Eisenstein series -- Ch. IV. The correspondence between forms of integral and half-integral weight -- Ch. V. The arithmeticity of critical values of Dirichlet series.
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