You are here: Home / Shop / Product Detail Page |

## Graduate Texts in Mathematics: A First Course in Modular Forms (Hardback)"This book introduces the theory of modular forms with an eye toward the Modularity Theorem: All rational elliptic curves arise from modular forms." — From the back cover ## $42.69 |

### Need More Info?

Please contact us if you've got questions about this product.## Condition

**LIKE NEW:** This book is in excellent, like-new condition. It was printed on acid-free paper.

## Description

From the back cover: “The topics covered include:

- 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 eignforms,
- the Galois representations associated to elliptic curves and 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.

“*A First Course in Modular Forms* is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.”

**Chapters**

- Modular Forms, Elliptic Curves, and Modular Curves
- Modular Curves as Riemann Surfaces
- Dimension Formulas
- Eisenstein Series
- Hecke Operators
- Jacobians and Abelian Varieties
- Modular Curves as Algebraic Curves
- The Eichler-Shimura Relation and
*L*-functions - Galois Representations

The book concludes with the sections **Hints and Answers to the Exercises**, **List of Symbols**, **Index**, and **References**.

## Details

- SKU:
- 2505
- Subject:
- Mathematics
- Author:
- Diamond, Fred and Jerry Shurman
- Publisher:
- Springer
- Publish Date:
- 2005 (First Printing)
- Format:
- Hardback
- Weight (pounds):
- 1.69
- Dimensions (W”xL”xH”):
- 6.3″x9.5″x1″
- ISBN-13:
- 9780387232294
- ISBN-10:
- 038723229X
- Grade Level:
- Graduate
- Series:
- Springer Graduate Texts in Mathematics

## Related Products

### Products related to "Graduate Texts in Mathematics: A First Course in Modular Forms (Hardback)"

- Views:

#### The MAA New Mathematical Library 20: Invitation to Number Theory (Softcover)

$13.97

"Number theory has been instrumental in introducing many of the most distinguished mathematicians, past and present, to the charms and mysteries of mathematical research. The purpose of this simple little guide will have been achieved if it should lead some of its readers to appreciate why the properties of numbers can be so fascinating. It would be better still if it would induce you to try to find some number relations of your own; new curiosities devised by young people turn up every year." — From the back cover

#### Cambridge Studies in Mathematics 14: An Introduction to the Theory of the Riemann Zeta-Function (Softcover)

$19.79

"This is a modern introduction to the analytic techniques used in the investigation of zeta-functions through the example of the Riemann zeta-function." — From the back cover

#### Graduate Texts in Mathematics: Introduction to Cyclotomic Fields, Second Edition (Hardback)

$57.95

"

*Introduction to Cyclotomic Fields*is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory." — From the back cover#### Disquisitiones Arithmeticae (Softcover)

$29.25

"The first translation into English of the standard work on the theory of numbers by one of the greatest masters of modern mathematical analysis, this classic was first published in 1801 in Latin. It has continued to be important to mathematicians as the source of the ideas from which modern number theory was developed and to students of the history of the mathematical sciences." — From the back cover

#### Student Mathematical Library, Volume 6: The Prime Numbers and Their Distribution (Softcover)

$10.39

"This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians." — From the back cover

#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Softcover)

$73.95

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### Undergraduate Texts in Mathematics: Elements of Algebra: Geometry, Numbers, Equations (Hardback)

$24.85

"This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory." — From the back cover

#### Zeta Functions of Graphs: A Stroll through the Garden (Hardback)

$43.95

"Graph theory meets number theory in this stimulating book." — From the back cover

#### Challenging Problems in Algebra (Softcover)

$5.99

"Designed for high-school students and teachers with an interest in mathematical problem-solving, this stimulating collection includes more than 300 problems that are 'off the beaten path'—i.e., problems that give a new twist to familiar topics or that introduce unfamiliar topics. With few exceptions, their solution requires little more than some knowledge of elementary algebra, though a dash of ingenuity may help." — From the back cover

#### The Theory of Partitions (Softcover)

$43.79

"This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive numbers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1." — From the back cover

#### Encyclopedia of Mathematics and Its Applications 94: Mathematical Constants (Hardback)

$47.39

"The pages of

*Mathematical Constants*abound in thousands of tales about numbers. This book is an amazing piece of erudition destined to fascinate the novice, puzzle the exerpt, and trigger the imagination of all." — the late Philippe Flajolet, renowned computer scientist#### Encyclopedia of Mathematics and Its Applications 20: Finite Fields (Hardback)

$123.50

"In this book, which is the first one devoted entirely to finite fields, we have aimed at presenting both the classical and the applications-oriented aspect of the subject. Thus, in addition to what has to be considered the essential core of the theory, the reader will find results and techniques that are of importance mainly because of their use in applications." — From the Authors in the Preface

#### An Invitation to Modern Number Theory (Hardback)

$47.49

"In a manner accessible to beginning undergraduates,

*An Invitation to Modern Number Theory*introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory." — From the back cover#### London Mathematical Society Student Texts 23: Complex Algebraic Curves (Softcover)

$45.89

"This book grew from a lecture course given by Dr Kirwan at Oxford University and will be an excellent companion for final year undergraduates and graduates who are studying complex algebraic curves." — From the back cover

#### Undergraduate Texts in Mathematics: Introduction to Analytic Number Theory (Hardback)

$33.95

"This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory." — From the back cover

#### Handbook of Mathematics and Computational Science (Hardback)

$39.50

"The Harris and Stocker Handbook of Mathematics and Computation Science is a complete desk-top reference for working scientists, engineers, and students. It serves as a veritable math toolbox for rapid access to a wealth of mathematics information for everyday use in problem solving, homework, examinations, etc." — From the back cover

#### Graduate Texts in Mathematics: Multiplicative Number Theory, Third Edition (Hardback)

$54.99

"This book thoroughly examines the distribution of prime numbers in arithmetic progressions." — From the back cover

#### The Queen of Mathematics: A Historically Motivated Guide to Number Theory (Hardback)

$49.50

"Starting in the fall of 1986, I combined my interests in number theory and history by teaching a one-year course in number theory from a historical prospective. The course used historical highlights to show the development of various topics, and I included some discussion about the lives of famous number theorists. My lecture notes for the course turned into a more formal set of notes, which turned into this book. Both the spirit and organization of material in the book remain those of my original lectures." — Jay R. Goldman, author, in the Preface

#### Elliptic Curves: Number Theory and Cryptography (Hardback)

$79.95

"Elliptic curves have played an increasingly important role in number theory and relate fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, an few are truly accessible to senior undergraduate or beginning graduate students. Assuming only a modest background in elementary number theory, groups, and fields,

*Elliptic Curves: Number Theory an Cryptography*introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications." — From the back cover#### Elementary Geometry of Algebraic Curves: An Undergraduate Introduction (Softcover)

$38.79

"This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences." — From the back cover