On the Theory of Maass Wave Forms

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.

• 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.

“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)