Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (7 chapters)
Keywords
About this book
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.
Reviews
“The book is essentially self-contained; the only prerequisites are basic knowledge of complex analysis, real analysis, and abstract algebra. For the convenience of the reader, the book includes an appendix with background material. … The main use of the book is probably for advanced master's or graduate students to learn about the theory of Maass wave forms. However, the book should also be useful for established researchers in mathematics or related disciplines to enter the field.” (Sander Zwegers, Mathematical Reviews, October, 2022)
“The level of the textbook is suitable for master students and so on, but some proofs can easily be understood by advanced undergraduate students.” (Ilker Inam, zbMATH 1456.11002, 2021)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: On the Theory of Maass Wave Forms
Authors: Tobias Mühlenbruch, Wissam Raji
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-030-40475-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-40477-2Published: 12 June 2020
eBook ISBN: 978-3-030-40475-8Published: 06 May 2020
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXV, 509
Number of Illustrations: 11 b/w illustrations
Topics: Number Theory