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Introduction to Modular Forms

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 472/5 ( reviews)

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Book Synopsis Introduction to Modular Forms by : Serge Lang

Download or read book Introduction to Modular Forms written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Modular Forms

2017-08-02 Mathematics
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Release : 2017-08-02
Genre : Mathematics
Kind : eBook
Book Rating : 476/5 ( reviews)

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Book Synopsis Modular Forms by : Henri Cohen

Download or read book Modular Forms written by Henri Cohen. This book was released on 2017-08-02. Available in PDF, EPUB and Kindle. Book excerpt: 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 being given in a separate chapter.

A First Course in Modular Forms

2006-03-30 Mathematics
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Release : 2006-03-30
Genre : Mathematics
Kind : eBook
Book Rating : 267/5 ( reviews)

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Book Synopsis A First Course in Modular Forms by : Fred Diamond

Download or read book A First Course in Modular Forms written by Fred Diamond. This book was released on 2006-03-30. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Introduction to Elliptic Curves and Modular Forms

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 099/5 ( reviews)

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Book Synopsis Introduction to Elliptic Curves and Modular Forms by : Neal I. Koblitz

Download or read book Introduction to Elliptic Curves and Modular Forms written by Neal I. Koblitz. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. This new edition details the current state of knowledge of elliptic curves.

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.

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