On the Theory of Maass Wave Forms. 1st ed. 2020

種類:

電子ブック

責任表示:

by Tobias Mühlenbruch, Wissam Raji

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Mühlenbruch, Tobias.
• Raji, Wissam.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783030404758 [3030404757]    

注記:

1. A Brief Introduction to Modular Forms -- 2. Period Polynomials -- 3. Maass Wave Forms of Real Weight -- 4. Families of Maass Cusp Forms, L-Series and Eichler Integrals -- 5. Period Functions -- 6. Continued Fractions and the Transfer Operator Approach -- 7. Weak Harmonic Maass Wave Forms -- A. Background Material -- References -- Symbol Index -- Index.
This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass W

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