Modular Forms And Fermat S Last Theorem

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Modular Forms and Fermat’s Last Theorem

Gary Cornell,Joseph H. Silverman,Glenn Stevens
Modular Forms and Fermat s Last Theorem Book PDF

Author : Gary Cornell,Joseph H. Silverman,Glenn Stevens
Publisher : Springer Science & Business Media
Page : 608 pages
File Size : 54,5 Mb
Release : 1997
Category : Mathematics
ISBN : 0387946098

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Modular Forms and Fermat’s Last Theorem by Gary Cornell,Joseph H. Silverman,Glenn Stevens Pdf

A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.

Modular Forms and Fermat’s Last Theorem

Gary Cornell,Joseph H. Silverman,Glenn Stevens
Modular Forms and Fermat s Last Theorem Book PDF

Author : Gary Cornell,Joseph H. Silverman,Glenn Stevens
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 48,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461219743

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Modular Forms and Fermat’s Last Theorem by Gary Cornell,Joseph H. Silverman,Glenn Stevens Pdf

This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Elliptic Curves, Modular Forms & Fermat's Last Theorem

John Coates,Shing-Tung Yau
Elliptic Curves Modular Forms Fermat s Last Theorem Book PDF

Author : John Coates,Shing-Tung Yau
Publisher : International Press of Boston
Page : 360 pages
File Size : 42,7 Mb
Release : 1997
Category : Mathematics
ISBN : UOM:39015043823981

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Elliptic Curves, Modular Forms & Fermat's Last Theorem by John Coates,Shing-Tung Yau Pdf

These proceedings are based on a conference at the Chinese University of Hong Kong, held in response to Andrew Wile's conjecture that every elliptic curve over Q is modular. The survey article describing Wile's work is included as the first article in the present edition.

A First Course in Modular Forms

Fred Diamond,Jerry Shurman
A First Course in Modular Forms Book PDF

Author : Fred Diamond,Jerry Shurman
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 41,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387272269

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A First Course in Modular Forms by Fred Diamond,Jerry Shurman Pdf

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.

Seminar on Fermat's Last Theorem

Vijaya Kumar Murty
Seminar on Fermat s Last Theorem Book PDF

Author : Vijaya Kumar Murty
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 46,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803134

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Seminar on Fermat's Last Theorem by Vijaya Kumar Murty Pdf

The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his work establishes a new reciprocity law. Reciprocity laws lie at the heart of number theory. Wiles' work draws on many of the tools of modern number theory and the purpose of this volume is to introduce readers to some of this background material. Based on a seminar held during 1993-1994 at the Fields Institute for Research in Mathematical Sciences, this book contains articles on elliptic curves, modular forms and modular curves, Serre's conjectures, Ribet's theorem, deformations of Galois representations, Euler systems, and annihilators of Selmer groups. All of the authors are well known in their field and have made significant contributions to the general area of elliptic curves, Galois representations, and modular forms. Features: Brings together a unique collection of number theoretic tools. Makes accessible the tools needed to understand one of the biggest breakthroughs in mathematics. Provides numerous references for further study.

13 Lectures on Fermat's Last Theorem

Paulo Ribenboim
13 Lectures on Fermat s Last Theorem Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493429

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13 Lectures on Fermat's Last Theorem by Paulo Ribenboim Pdf

Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.

Fermat's Last Theorem

Takeshi Saitō
Fermat s Last Theorem Book PDF

Author : Takeshi Saitō
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 43,5 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9780821898482

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Fermat's Last Theorem by Takeshi Saitō Pdf

This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

Fermat’s Last Theorem for Amateurs

Paulo Ribenboim
Fermat s Last Theorem for Amateurs Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 407 pages
File Size : 47,5 Mb
Release : 2008-01-21
Category : Mathematics
ISBN : 9780387216928

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Fermat’s Last Theorem for Amateurs by Paulo Ribenboim Pdf

In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.

Algebraic Number Theory and Fermat's Last Theorem

Ian Stewart,David Tall
Algebraic Number Theory and Fermat s Last Theorem Book PDF

Author : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 49,5 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081

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Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart,David Tall Pdf

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

Fermat's Last Theorem

Simon Singh
Fermat s Last Theorem Book PDF

Author : Simon Singh
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 1998-05
Category : Electronic
ISBN : 1857029224

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Fermat's Last Theorem by Simon Singh Pdf

In 1963 a schoolboy browsing in his local library stumbled across a great mathematical problem: Fermat's Last Theorem, a puzzle that every child can now understand, but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed he would crack it.

The 1-2-3 of Modular Forms

Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier
The 1 2 3 of Modular Forms Book PDF

Author : Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 53,6 Mb
Release : 2008-02-10
Category : Mathematics
ISBN : 9783540741190

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The 1-2-3 of Modular Forms by Jan Hendrik Bruinier,Gerard van der Geer,Günter Harder,Don Zagier Pdf

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Invitation to the Mathematics of Fermat-Wiles

Yves Hellegouarch
Invitation to the Mathematics of Fermat Wiles Book PDF

Author : Yves Hellegouarch
Publisher : Elsevier
Page : 395 pages
File Size : 41,7 Mb
Release : 2001-09-24
Category : Mathematics
ISBN : 9780080478777

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Invitation to the Mathematics of Fermat-Wiles by Yves Hellegouarch Pdf

Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem

Elliptic Curves, Modular Forms, and Their L-functions

Alvaro Lozano-Robledo
Elliptic Curves Modular Forms and Their L functions Book PDF

Author : Alvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 195 pages
File Size : 49,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852422

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Elliptic Curves, Modular Forms, and Their L-functions by Alvaro Lozano-Robledo Pdf

Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

Heads in Grammatical Theory

Greville G. Corbett,Norman M. Fraser,Scott McGlashan
Heads in Grammatical Theory Book PDF

Author : Greville G. Corbett,Norman M. Fraser,Scott McGlashan
Publisher : Cambridge University Press
Page : 364 pages
File Size : 52,5 Mb
Release : 1993-06-24
Category : Language Arts & Disciplines
ISBN : 052140245X

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Heads in Grammatical Theory by Greville G. Corbett,Norman M. Fraser,Scott McGlashan Pdf

A study of the idea of the 'head' or dominating element of a phrase.

The Last Theorem

Arthur C. Clarke,Frederik Pohl
The Last Theorem Book PDF

Author : Arthur C. Clarke,Frederik Pohl
Publisher : HarperCollins UK
Page : 23 pages
File Size : 47,6 Mb
Release : 2008-12-07
Category : Fiction
ISBN : 9780007308149

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The Last Theorem by Arthur C. Clarke,Frederik Pohl Pdf

The final work from the brightest star in science fiction’s galaxy. Arthur C Clarke, who predicted the advent of communication satellites and author of 2001: A Space Odyssey completes a lifetime career in science fiction with a masterwork.