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Modular forms and Hecke operators

1995-08-28 Mathematics
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Release : 1995-08-28
Genre : Mathematics
Kind : eBook
Book Rating : 621/5 ( reviews)

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Book Synopsis Modular forms and Hecke operators by : A. N. Andrianov V. G. Zhuravlev

Download or read book Modular forms and Hecke operators written by A. N. Andrianov V. G. Zhuravlev. This book was released on 1995-08-28. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.

Modular Forms and Hecke Operators

2016-01-29
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Release : 2016-01-29
Genre :
Kind : eBook
Book Rating : 681/5 ( reviews)

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Book Synopsis Modular Forms and Hecke Operators by : A. N. Andrianov

Download or read book Modular Forms and Hecke Operators written by A. N. Andrianov. This book was released on 2016-01-29. Available in PDF, EPUB and Kindle. Book excerpt: he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.

Modular Forms

2006-02-17 Mathematics
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Release : 2006-02-17
Genre : Mathematics
Kind : eBook
Book Rating : 933/5 ( reviews)

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Book Synopsis Modular Forms by : Toshitsune Miyake

Download or read book Modular Forms written by Toshitsune Miyake. This book was released on 2006-02-17. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition. It offers the basic knowledge of elliptic modular forms necessary to understand recent developments in number theory. It also treats the unit groups of quaternion algebras, rarely dealt with in books; and in the last chapter, Eisenstein series with parameter are discussed following the recent work of Shimura.

Modular Forms: A Classical And Computational Introduction (2nd Edition)

2015-03-12 Mathematics
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Release : 2015-03-12
Genre : Mathematics
Kind : eBook
Book Rating : 477/5 ( reviews)

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Book Synopsis Modular Forms: A Classical And Computational Introduction (2nd Edition) by : Lloyd James Peter Kilford

Download or read book Modular Forms: A Classical And Computational Introduction (2nd Edition) written by Lloyd James Peter Kilford. This book was released on 2015-03-12. Available in PDF, EPUB and Kindle. Book excerpt: Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

Quadratic Forms and Hecke Operators

1987-03-17 Mathematics
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Release : 1987-03-17
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Quadratic Forms and Hecke Operators by : Anatolij N. Andrianov

Download or read book Quadratic Forms and Hecke Operators written by Anatolij N. Andrianov. This book was released on 1987-03-17. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present the contemporary state of theory of Hecke operators on the spaces of holomorphic modular forms of integral weight (the Siegel modular forms) for congruence subgroups of integral symplectic groups. In this book Hecke operators are mainly considered as a tool for the investigation of multiplicative properties of Fourier coefficients of modular forms, in accordance with the initial approach of Hecke. The book is designed for those who wish to work in the arithmetical theory of automorphic forms, for those working in the field, or those who merely want to look into it. No special knowledge is assumed beyond the standard university courses in algebra (general and linear) and analysis (real and complex). The classical case of one variable is included.

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