Overview
The first book available on modular forms dealing with integral and half-integral weights in a unified framework
The first book dealing with in detail Eisenstein series with half-integral weights
Includes all necessary basic material for reading modern research literature on modular forms with half-integral weights
Offers some very beautiful applications of modular forms of half-integral weights to some arithmetic problems of definite positive quadratic forms
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics.
Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.
Reviews
From the book reviews:
“The book contains ten chapters. … this book is a welcome addition for the graduate student or the senior level undergraduate who is looking for a friendly introduction to the topic of modular forms. The book would be ideal for a one-term graduate course or an upper level undergraduate course.” (M. Ram Murty, Mathematical Reviews, May, 2014)
“The reader will find a thorough introduction to many central themes in the theory of modular forms of integral and half-integral weight in one variable. … This monograph is a very valuable addition to the literature on modular forms which will be useful for scholars and for graduate students in this very active branch of number theory.” (Günter Köhler, Zentralblatt MATH, Vol. 1263, 2013)Authors and Affiliations
Bibliographic Information
Book Title: Modular Forms with Integral and Half-Integral Weights
Authors: Xueli Wang, Dingyi Pei
DOI: https://doi.org/10.1007/978-3-642-29302-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Science Press, Beijing and Springer Berlin Heidelberg 2012
eBook ISBN: 978-3-642-29302-3Published: 20 February 2013
Edition Number: 1
Number of Pages: X, 432
Number of Illustrations: 2 b/w illustrations
Topics: Number Theory, Algebraic Geometry, Functions of a Complex Variable