About this book
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.
Modular forms Maass wave forms Eichler integrals Eichler-Shimura isomorphism L-series Period problems Period functions Maass wave forms of real weight Families of Maass cusp forms Transfer operator approach Weak harmonic Maass wave forms
- Book Title On the Theory of Maass Wave Forms
- Series Title Universitext
- Series Abbreviated Title Universitext
- DOI https://doi.org/10.1007/978-3-030-40475-8
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-030-40474-1
- Softcover ISBN 978-3-030-40477-2
- eBook ISBN 978-3-030-40475-8
- Series ISSN 0172-5939
- Series E-ISSN 2191-6675
- Edition Number 1
- Number of Pages XXV, 509
- Number of Illustrations 11 b/w illustrations, 0 illustrations in colour
- Buy this book on publisher's site
“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)