Modular Forms with Integral and Half-Integral Weights
Seiten
2012
|
2013
Springer Berlin (Verlag)
978-3-642-29301-6 (ISBN)
Springer Berlin (Verlag)
978-3-642-29301-6 (ISBN)
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Taking the theory of Eisenstein series as its core theme, this volume focuses on the fundamental principles of modular forms of one variable. With analysis of half-integral as well as integral weights, it is the first unified treatment to cover both in such detail.
"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.
"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.
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.
| Zusatzinfo | X, 432 p. 2 illus. |
|---|---|
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 730 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Schlagworte | Eisenstein series • Half-integral weights • Modular Forms • quadratic forms |
| ISBN-10 | 3-642-29301-8 / 3642293018 |
| ISBN-13 | 978-3-642-29301-6 / 9783642293016 |
| Zustand | Neuware |
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