Modular Forms: A Classical Approach (Graduate Studies in Mathematics, 179, Band 179) - Hardcover

Buch 143�von 190: Graduate Studies in Mathematics

Cohen, Henri ; Stromberg, Fredrik

9780821849477: Modular Forms: A Classical Approach (Graduate Studies in Mathematics, 179, Band 179)

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ISBN 10: 0821849476 ISBN 13: 9780821849477

Verlag: American Mathematical Society, 2017

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Updating material from courses they have taught at various times and places, Cohen and Str�mberg present an extremely classical account of modular forms, but also include many recent results in order to present a more complete picture of the current state of the art in the theory of modular forms and related topics. Some of these results appear in print for the first time here. Among the topics are basic tools, general aspects of holomorphic and nonholomorphic modular forms, modular forms and functions on subgroups, Hecke operators and Euler products, and an introduction to more general modular forms. Annotation �2017 Ringgold, Inc., Portland, OR (protoview.com)

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

�ber die Autorin bzw. den Autor

Henri Cohen, Universite Bordeaux, France.

Fredrik Stromberg, University of Nottingham, United Kingdom.

��ber diesen Titel� kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag: American Mathematical Society
Erscheinungsdatum: 2017
Sprache: Englisch
ISBN 10: 0821849476
ISBN 13: 9780821849477
Einband: Gebundene Ausgabe
Anzahl der Seiten: 700
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Henri Cohen

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Cohen, Henri; Stromberg, Fredrik

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Modular Forms (Hardcover)

Henri Cohen

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Hardcover. Zustand: new. Hardcover. The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and "fun" subject in itself and abounds with an amazing number of surprising identities.This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin-Lehner-Li theory of newforms and including the theory of Eisenstein series, Rankin-Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms.Some "gems" of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms.This book is essentially self-contained; the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on are given in a separate chapter. This comprehensive textbook, which includes numerous exercises, gives a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin-Lehner-Li theory of newforms and including the theory of Eisenstein series, Rankin-Selberg theory, and a more general theory of theta series. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verk�ufers 9780821849477

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Modular Forms : A Classical Approach

Cohen, Henri; Stromberg, Fredrik

Verlag: American Mathematical Society, 2017

ISBN 10: 0821849476 ISBN 13: 9780821849477

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Modular Forms

Henri Cohen, Fredrik Stromberg

Verlag: American Mathematical Society, US, 2017

ISBN 10: 0821849476 ISBN 13: 9780821849477

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Hardback. Zustand: New. The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and "fun" subject in itself and abounds with an amazing number of surprising identities.This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin-Lehner-Li theory of newforms and including the theory of Eisenstein series, Rankin-Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms.Some "gems" of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms.This book is essentially self-contained; the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on are given in a separate chapter. Bestandsnummer des Verk�ufers LU-9780821849477

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