On the theory of Maass wave forms / Tobias Mühlenbruch, Wissam Raji.
2020
QA243
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Title
On the theory of Maass wave forms / Tobias Mühlenbruch, Wissam Raji.
Author
Mühlenbruch, Tobias.
ISBN
9783030404758 (electronic book)
3030404757 (electronic book)
9783030404741
3030404749
3030404757 (electronic book)
9783030404741
3030404749
Publication Details
Cham : Springer, 2020.
Language
English
Description
1 online resource (527 pages).
Item Number
10.1007/978-3-030-40
10.1007/978-3-030-40475-8 doi
10.1007/978-3-030-40475-8 doi
Call Number
QA243
Dewey Decimal Classification
512.7/3
Summary
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 books 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 Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.
Bibliography, etc. Note
Includes bibliographical references and indexes.
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Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Description based on print version record.
Added Author
Raji, Wissam.
Series
Universitext.
Available in Other Form
On the Theory of Maass Wave Forms
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Table of Contents
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.
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.