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## Details

Additional Physical Format: | Modular Forms with Integral and Half-Integral Weights [Texte imprimé] 9783642293016 |
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Document Type: | Computer File |

All Authors / Contributors: |
Xueli Wang; Dingyi Pei |

ISBN: | 9783642293023 3642293026 |

OCLC Number: | 863598849 |

Description: | 1 online resource. |

Details: | NeÌcessite un lecteur de fichier PDF. |

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 |

Responsibility: | by Xueli Wang, Dingyi Pei. |

### Abstract:

"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.

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