Modular Forms with Integral and Half-Integral Weights
By: by Xueli Wang, Dingyi Pei
Contributors: Pei, Dingyi; SpringerLink (Online service)
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2012
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 400
ISBN-13: 9783642293023
Subjects: Mathematics; Algebraic Geometry; Functions of complex variables; Number theory
Description: "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.
Table of contents: title: Theta Functions and Their Transformation Formulae; title: Eisenstein Series; title: The Modular Group and Its Subgroups; title: Modular Forms with Integral Weight or Half-integral Weight; title: Operators on the Space of Modular Forms; title: New Forms and Old Forms.-Construction of Eisenstein Series; title: Weil Representation and Shimura Lifting; title: Trace Formula; title: Integers Represented by Positive Definite Quadratic Forms.