Modular Forms with Integral and Half-Integral Weights
(Sprache: Englisch)
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.
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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.
Klappentext zu „Modular Forms with Integral and Half-Integral Weights “
"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.
Inhaltsverzeichnis zu „Modular Forms with Integral and Half-Integral Weights “
- 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
Bibliographische Angaben
- Autoren: Xueli Wang , Dingyi Pei
- 2013, 432 Seiten, 2 Schwarz-Weiß-Abbildungen, Maße: 15,5 x 23,5 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3642293018
- ISBN-13: 9783642293016
- Erscheinungsdatum: 07.09.2012
Sprache:
Englisch
Rezension zu „Modular Forms with Integral and Half-Integral Weights “
From the reviews:"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
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