Silverman, Joseph H. 1955
Overview
Works:  29 works in 372 publications in 5 languages and 8,960 library holdings 

Genres:  Conference papers and proceedings Textbooks 
Roles:  Author, Editor, Other, Contributor, Creator 
Classifications:  QA241, 512.7 
Publication Timeline
.
Most widely held works by
Joseph H Silverman
The arithmetic of elliptic curves by
Joseph H Silverman(
Book
)
55 editions published between 1985 and 2011 in English and Undetermined and held by 937 WorldCat member libraries worldwide
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebrogeometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the MordellWeil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics
55 editions published between 1985 and 2011 in English and Undetermined and held by 937 WorldCat member libraries worldwide
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebrogeometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the MordellWeil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics
Rational points on elliptic curves by
Joseph H Silverman(
Book
)
39 editions published between 1992 and 2015 in English and German and held by 709 WorldCat member libraries worldwide
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and group structure of elliptic curves, the NagellLutz theorem describing points of finite order, the MordellWeil theorem on the finite generation of the group of rational points, the ThueSiegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves
39 editions published between 1992 and 2015 in English and German and held by 709 WorldCat member libraries worldwide
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and group structure of elliptic curves, the NagellLutz theorem describing points of finite order, the MordellWeil theorem on the finite generation of the group of rational points, the ThueSiegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves
A friendly introduction to number theory by
Joseph H Silverman(
Book
)
54 editions published between 1997 and 2018 in 4 languages and held by 661 WorldCat member libraries worldwide
Ben shu jiang shu le you guan shu lun da liang you qu de zhi shi,Yi ji shu lun de yi ban fang fa he ying yong,Xun xu jian jin di qi fa du zhe yong shu xue fang fa si kao wen ti,Hai jie shao le mu qian shu lun yan jiu de mou xie qian yan ke ti
54 editions published between 1997 and 2018 in 4 languages and held by 661 WorldCat member libraries worldwide
Ben shu jiang shu le you guan shu lun da liang you qu de zhi shi,Yi ji shu lun de yi ban fang fa he ying yong,Xun xu jian jin di qi fa du zhe yong shu xue fang fa si kao wen ti,Hai jie shao le mu qian shu lun yan jiu de mou xie qian yan ke ti
Diophantus and diophantine equations by
I. G Bashmakova(
Book
)
7 editions published in 1997 in English and held by 657 WorldCat member libraries worldwide
7 editions published in 1997 in English and held by 657 WorldCat member libraries worldwide
An introduction to mathematical cryptography by
Jeffrey Hoffstein(
Book
)
43 editions published between 2008 and 2014 in English and held by 532 WorldCat member libraries worldwide
"This selfcontained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic filter algebra is requited of the reader; techniques from algebra, number theory, and probability are introduced and developed as required."Back cover
43 editions published between 2008 and 2014 in English and held by 532 WorldCat member libraries worldwide
"This selfcontained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic filter algebra is requited of the reader; techniques from algebra, number theory, and probability are introduced and developed as required."Back cover
Modular forms and Fermat's last theorem(
Book
)
20 editions published between 1997 and 2007 in English and Undetermined and held by 531 WorldCat member libraries worldwide
"The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the LanglandsTunnell theorem, and this is followed by indepth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections, and more, as the reader is led stepbystep through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epochmaking proof of Fermat's Last Theorem."Jacket
20 editions published between 1997 and 2007 in English and Undetermined and held by 531 WorldCat member libraries worldwide
"The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the LanglandsTunnell theorem, and this is followed by indepth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections, and more, as the reader is led stepbystep through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, 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 volume to be an indispensable resource for mastering the epochmaking proof of Fermat's Last Theorem."Jacket
Advanced topics in the arithmetic of elliptic curves by
Joseph H Silverman(
Book
)
28 editions published between 1994 and 2011 in English and Undetermined and held by 506 WorldCat member libraries worldwide
In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the MordellWeil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, KodairaN ron classification of special fibres, Tate's algorithm, and Ogg's conductordiscriminant formula. V. Tate's theory of qcurves over padic fields. VI. Néron's theory of canonical local height functions
28 editions published between 1994 and 2011 in English and Undetermined and held by 506 WorldCat member libraries worldwide
In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the MordellWeil theorem on the finite generation of the group of rational points and Siegel's theorem on the finiteness of the set of integral points. This book continues the study of elliptic curves by presenting six important, but somewhat more specialized topics: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Néron models, KodairaN ron classification of special fibres, Tate's algorithm, and Ogg's conductordiscriminant formula. V. Tate's theory of qcurves over padic fields. VI. Néron's theory of canonical local height functions
Diophantine geometry : an introduction by
Marc Hindry(
Book
)
15 editions published between 2000 and 2010 in English and held by 420 WorldCat member libraries worldwide
"Diophantine geometry is the study of integral and rational solutions to systems of polynomial equations using ideas and techniques from algebraic number theory and algebraic geometry. The ultimate goal is to describe the solutions in terms of geometric invariants of the underlying algebraic variety. This book contains complete proofs of four of the fundamental finiteness theorems in Diophantine geometry."Jacket
15 editions published between 2000 and 2010 in English and held by 420 WorldCat member libraries worldwide
"Diophantine geometry is the study of integral and rational solutions to systems of polynomial equations using ideas and techniques from algebraic number theory and algebraic geometry. The ultimate goal is to describe the solutions in terms of geometric invariants of the underlying algebraic variety. This book contains complete proofs of four of the fundamental finiteness theorems in Diophantine geometry."Jacket
An introduction to the theory of numbers by
G. H Hardy(
Book
)
10 editions published between 2008 and 2010 in English and Chinese and held by 380 WorldCat member libraries worldwide
The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated endofchapter notes
10 editions published between 2008 and 2010 in English and Chinese and held by 380 WorldCat member libraries worldwide
The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated endofchapter notes
Arithmetic geometry by
Gary Cornell(
Book
)
17 editions published between 1986 and 1998 in English and held by 377 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
17 editions published between 1986 and 1998 in English and held by 377 WorldCat member libraries worldwide
This book is the result of a conference on arithmetic geometry, held July 30 through August 10, 1984 at the University of Connecticut at Storrs, the purpose of which was to provide a coherent overview of the subject. This subject has enjoyed a resurgence in popularity due in part to Faltings' proof of Mordell's conjecture. Included are extended versions of almost all of the instructional lectures and, in addition, a translation into English of Faltings' groundbreaking paper. ARITHMETIC GEOMETRY should be of great use to students wishing to enter this field, as well as those already working in it. This revised second printing now includes a comprehensive index
The arithmetic of dynamical systems by
Joseph H Silverman(
Book
)
20 editions published between 2007 and 2011 in English and held by 346 WorldCat member libraries worldwide
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of selfmaps of the complex plane or real line, arithmetic dynamics is the study of the numbertheoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures
20 editions published between 2007 and 2011 in English and held by 346 WorldCat member libraries worldwide
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of selfmaps of the complex plane or real line, arithmetic dynamics is the study of the numbertheoretic properties of rational and algebraic points under repeated application of a polynomial or rational function. A principal theme of arithmetic dynamics is that many of the fundamental problems in the theory of Diophantine equations have dynamical analogs. As is typical in any subject combining Diophantine problems and geometry, a fundamental goal is to describe arithmetic properties, at least qualitatively, in terms of underlying geometric structures
Cryptography and lattices : international conference, CaLC 2001, Providence RI, USA, March 2930, 2001 : revised papers by
Joseph H Silverman(
Book
)
23 editions published in 2001 in English and held by 265 WorldCat member libraries worldwide
This book constitutes the thoroughly refereed postproceedings of the International Conference on Cryptography and Lattices, CaLC 2001, held in Providence, RI, USA in March 2001. The 14 revised full papers presented together with an overview paper were carefully reviewed and selected for inclusion in the book. All current aspects of lattices and lattice reduction in cryptography, both for cryptographic construction and cryptographic analysis, are addressed
23 editions published in 2001 in English and held by 265 WorldCat member libraries worldwide
This book constitutes the thoroughly refereed postproceedings of the International Conference on Cryptography and Lattices, CaLC 2001, held in Providence, RI, USA in March 2001. The 14 revised full papers presented together with an overview paper were carefully reviewed and selected for inclusion in the book. All current aspects of lattices and lattice reduction in cryptography, both for cryptographic construction and cryptographic analysis, are addressed
Moduli spaces and arithmetic dynamics by
Joseph H Silverman(
Book
)
8 editions published in 2012 in English and held by 141 WorldCat member libraries worldwide
8 editions published in 2012 in English and held by 141 WorldCat member libraries worldwide
The arithmetic of elliptic curves II by
Joseph H Silverman(
Book
)
2 editions published in 1994 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 8 WorldCat member libraries worldwide
The NéronTate height on elliptic curves by
Joseph H Silverman(
)
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
Folk literature of the Sephardic Jews(
Book
)
in English and held by 3 WorldCat member libraries worldwide
in English and held by 3 WorldCat member libraries worldwide
Daen kyokusen ron nyūmon(
Book
)
3 editions published between 1995 and 2012 in Japanese and held by 3 WorldCat member libraries worldwide
3 editions published between 1995 and 2012 in Japanese and held by 3 WorldCat member libraries worldwide
LOW FREQUENCY GYRATOR DEVELOPMENT(
Book
)
2 editions published between 1961 and 1962 in English and held by 2 WorldCat member libraries worldwide
Network synthesis of series and parallel neutralizing net orks is described and results presented. Effect of these networks on pass direceved by adding a single reactance in parallel or series with the EM gyrator. EM gyrators, each consisting of a magnetostrictive ferrite plate bonded to a piezoelectric plate, were designed using composite beam theory. These structures perform well in both flexural and longitudinal modes, and hence cover a wide fr tion insertion loss is examined theoretically. An efficient isolator, with a narrow band of rejection in the stop direction and low insertion loss in the pass direction, is achieved by adding a single reactance in parallel or series with the EM gyrator. EM gyrators, each consisting of a magnetostrictive ferrite plate bonded to a piezoelectric plate, were designed using composite beam theory. These structures perform well in both flexural and longitudinal modes, and hence cover a wide frequency range. In both cases, signal takeoff from the magnetostrictive bar is effected by a coil wrapped either around the ferrite (before bonding) or around the composite structure. Optimum bias for the ferrite is provided by strategic location of a permanent magnetic. A second type of EM gyrator, consisting of an electrodynamic transducer coupled to a piezoelectric Bimorph, was investigated and found to be far less efficient than the piezoelectricpiezomagnetic system. (Author)
2 editions published between 1961 and 1962 in English and held by 2 WorldCat member libraries worldwide
Network synthesis of series and parallel neutralizing net orks is described and results presented. Effect of these networks on pass direceved by adding a single reactance in parallel or series with the EM gyrator. EM gyrators, each consisting of a magnetostrictive ferrite plate bonded to a piezoelectric plate, were designed using composite beam theory. These structures perform well in both flexural and longitudinal modes, and hence cover a wide fr tion insertion loss is examined theoretically. An efficient isolator, with a narrow band of rejection in the stop direction and low insertion loss in the pass direction, is achieved by adding a single reactance in parallel or series with the EM gyrator. EM gyrators, each consisting of a magnetostrictive ferrite plate bonded to a piezoelectric plate, were designed using composite beam theory. These structures perform well in both flexural and longitudinal modes, and hence cover a wide frequency range. In both cases, signal takeoff from the magnetostrictive bar is effected by a coil wrapped either around the ferrite (before bonding) or around the composite structure. Optimum bias for the ferrite is provided by strategic location of a permanent magnetic. A second type of EM gyrator, consisting of an electrodynamic transducer coupled to a piezoelectric Bimorph, was investigated and found to be far less efficient than the piezoelectricpiezomagnetic system. (Author)
Daen kyokusen ron gaisetsu by
Joseph H Silverman(
Book
)
4 editions published in 2003 in Japanese and held by 2 WorldCat member libraries worldwide
4 editions published in 2003 in Japanese and held by 2 WorldCat member libraries worldwide
Introduction to Mathematical Cryptography, An. Undergraduate Texts in Mathematics(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Offers an introduction to modern cryptography that emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. This book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Offers an introduction to modern cryptography that emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. This book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems
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Related Identities
 Pipher, Jill Catherine 1955 Contributor
 Hoffstein, Jeffrey Author
 Cornell, Gary Other Author Editor
 Tate, John Torrence 1925 Author Creator
 Bashmakova, I. G. (Izabella Grigorʹevna) Author
 Stevens, Glenn 1953 Other Editor
 Hindry, Marc Author
 HeathBrown, D. R. Editor
 Hardy, G. H. (Godfrey Harold) 18771947 Author
 Wright, Edward Maitland 1906
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Associated Subjects
Algebra AlgebraData processing Algebraic number theory Algorithms Analytic spaces Arithmetic Arithmetical algebraic geometry Coding theory Computational complexity Computer science Computer software Congruences and residues Continued fractions Cryptography CryptographyMathematics Curves, Algebraic Curves, Elliptic Data encryption (Computer science) Data structures (Computer science) Differentiable dynamical systems Diophantine analysis Diophantine equations Dynamics Elliptic functions Ergodic theory Fermat's last theorem Fermat's theorem Forms, Modular Fundamental theorem of algebra Geometry Geometry, Algebraic Geometry of numbers Harmonic analysis Information theory Irrational numbers Lattice theory Mathematics Moduli theory Number theory Ordered algebraic structures Partitions (Mathematics) Quadratic fields Rational points (Geometry) Series Signs and symbols Tate, John Torrence,
Alternative Names
Joseph H. Silverman amerikansk matematikar
Joseph H. Silverman amerikansk matematiker
Joseph H. Silverman matemático estadounidense
Joseph H. Silverman matematico statunitense
Joseph Hillel Silverman
Joseph Silverman Amerikaans wiskundige
Joseph Silverman mathématicien américain
Joseph Silverman USamerikanischer Mathematiker
Silverman, J.
Silverman, J. 1955
Silverman, J. H.
Silverman, J. H. 1955
Silverman, J. H. (Joseph H.), 1955
Silverman, Joseph
Silverman, Joseph 1955
Silverman, Joseph H.
Джозеф Сильверман американский математик
جوزف اچ. سیلورمن ریاضیدان آمریکایی
실버만, 조셉
실버만, 조셉 H
ジョゼフ・シルバーマン
シルヴァーマン, J. H
シルヴァーマン, ジョセフ・H
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Covers