Modular Forms with Integral and Half-Integral Weights

• Main Authors: Wang, Xueli (Author), Pei, Dingyi (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Subjects: Mathematics.; Algebraic geometry.; Functions of complex variables.; Number theory.; Number Theory.; Algebraic Geometry.; Functions of a Complex Variable.

"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 orthogo...

Table of Contents:

• 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.