Modular Forms with Integral and Half-Integral Weights
Wang, Xueli, Pei, Dingyi
2013, X, 432 p.
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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
"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.
Content Level »Research
Keywords »Eisenstein series - Half-integral weights - Modular forms - Quadratic forms
Theta Functions and Their Transformation Formulae.- Eisenstein Series.- The Modular Group and Its Subgroups.- Modular Forms with Integral Weight or Half-integral Weight.- Operators on the Space of Modular Forms.- New Forms and Old Forms.-Construction of Eisenstein Series.- Weil Representation and Shimura Lifting.- Trace Formula.- Integers Represented by Positive Definite Quadratic Forms.