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On the Theory of Maass Wave Forms

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the Theory of Maass Wave Forms/ by Tobias Mühlenbruch, Wissam Raji.
Author:	Mühlenbruch, Tobias.
other author:	Raji, Wissam.
Description:	XXV, 509 p. 11 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Number theory. -
Online resource:	https://doi.org/10.1007/978-3-030-40475-8
ISBN:	9783030404758

On the Theory of Maass Wave Forms
Mühlenbruch, Tobias.

On the Theory of Maass Wave Forms[electronic resource] /by Tobias Mühlenbruch, Wissam Raji. - 1st ed. 2020. - XXV, 509 p. 11 illus.online resource. - Universitext,0172-5939. - Universitext,.

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.

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.

ISBN: 9783030404758

Standard No.: 10.1007/978-3-030-40475-8doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241-247.5

Dewey Class. No.: 512.7

On the Theory of Maass Wave Forms
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520 $a 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.
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