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On the theory of Maass wave forms

Muhlenbruch, Tobias.

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On the theory of Maass wave forms

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the theory of Maass wave forms/ by Tobias Muhlenbruch, Wissam Raji.
作者:	Muhlenbruch, Tobias.
其他作者:	Raji, Wissam.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xxv, 509 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Forms, Modular. -
電子資源:	https://doi.org/10.1007/978-3-030-40475-8
ISBN:	9783030404758

On the theory of Maass wave forms
Muhlenbruch, Tobias.

On the theory of Maass wave forms[electronic resource] /by Tobias Muhlenbruch, Wissam Raji. - Cham :Springer International Publishing :2020. - xxv, 509 p. :ill., digital ;24 cm. - 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:

540521
Forms, Modular.

LC Class. No.: QA243 / .M865 2020

Dewey Class. No.: 512.73

On the theory of Maass wave forms
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505 0 $a 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.
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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