On the theory of Maass wave forms / Tobias Mühlenbruch, Wissam Raji.

Format:

Book

Author/Creator:

Mühlenbruch, Tobias, author.

Raji, Wissam, author.

Series:

Universitext 0172-5939

Universitext, 0172-5939

Language:

English

Subjects (All):

Forms, Modular.

Forms (Mathematics).

Wave functions.

Holomorphic functions.

Number theory.

Physical Description:

xxv, 509 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2020]

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"--Back cover.

Contents:

A Brief Introduction to Modular Forms

Period Polynomials

Maass Wave Forms of Real Weight

Families of Maass Cusp Forms, L-Series and Eichler Integrals

Period Functions

Continued Fractions and the Transfer Operator Approach

Weak Harmonic Maass Wave Forms

Background Material.

Notes:

Includes bibliographical references and indexes.

ISBN:

9783030404772

3030404773

OCLC:

1135391723