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Universitext

On the Theory of Maass Wave Forms

Authors: Mühlenbruch, Tobias, Raji, Wissam

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  • Provides a rigorous analytical treatment of the theory of Maass wave forms
  • Presents a self-contained exploration of the topic, from a brief review of introductory concepts through to cutting edge research
  • Offers readers a number of insightful exercises with solutions available online
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  • ISBN 978-3-030-40475-8
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Softcover $59.99
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  • ISBN 978-3-030-40477-2
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About this Textbook

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 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.

About the authors

Tobias Mühlenbruch is a private lecturer at the FernUniversität in Hagen, Germany. His main research interest include number theory with a focus on analytic modular forms and the connections to dynamical systems and mathematical physics. 

Wissam Raji is an Associate Professor of Mathematics at the American University of Beirut, Lebanon. His research interests include analytic number theory and modular forms with a focus on period polynomials. He is the recipient of numerous awards, including the Saylor Foundation’s 2013 Open Textbook Challenge.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-3-030-40475-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
  • ISBN 978-3-030-40477-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
On the Theory of Maass Wave Forms
Authors
Series Title
Universitext
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-40475-8
DOI
10.1007/978-3-030-40475-8
Softcover ISBN
978-3-030-40477-2
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XXV, 509
Number of Illustrations
11 b/w illustrations
Topics

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