Silverman, Joseph H. 1955Overview
Publication Timeline
Most widely held works by
Joseph H Silverman
The arithmetic of elliptic curves
by Joseph H Silverman
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Book
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64 editions published between 1985 and 2011 in English and held by 1,701 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, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX. 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
An introduction to mathematical cryptography
by Jeffrey Hoffstein
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20 editions published between 2008 and 2010 in English and held by 963 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 linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: @* classical cryptographic constructions, such as DiffieHellmann key exchange, discrete logarithmbased cryptosystems, the RSA cryptosystem, and digital signatures; @* fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; @* an indepth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairingbased cryptography, lattices, latticebased cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online
Diophantus and diophantine equations
by I. G Bashmakova
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6 editions published in 1997 in English and held by 655 WorldCat member libraries worldwide
Rational points on elliptic curves
by Joseph H Silverman
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22 editions published between 1992 and 2011 in 3 languages and held by 626 WorldCat member libraries worldwide The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" stresses this interplay as it develops the basic theory, thereby providing an opportunity for advance 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
The arithmetic of dynamical systems
by Joseph H Silverman
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19 editions published between 2007 and 2011 in English and held by 608 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
A friendly introduction to number theory
by Joseph H Silverman
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34 editions published between 1997 and 2013 in English and held by 581 WorldCat member libraries worldwide
Modular forms and Fermat's last theorem
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17 editions published between 1997 and 2007 in English and Undetermined and held by 506 WorldCat member libraries worldwide The book will focus on two major topics: Andrew Wiles' recent proof of the TaniyamaShimuraWeil conjecture for semistable elliptic curves; and the earlier works of Frey, Serre, Ribet  showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem
Diophantine geometry : an introduction
by Marc Hindry
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11 editions published between 2000 and 2010 in English and held by 407 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."BOOK JACKET
Arithmetic geometry
by Gary Cornell
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13 editions published between 1986 and 1998 in English and held by 385 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
An introduction to the theory of numbers
by G. H Hardy
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Book
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8 editions published between 2008 and 2009 in English and held by 352 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
Cryptography and lattices : international conference, CaLC 2001, Providence RI, USA, March 2930, 2001 : revised papers
by CaLC 2001
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11 editions published in 2001 in English and held by 285 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
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6 editions published in 2012 in English and held by 123 WorldCat member libraries worldwide
The arithmetic of elliptic curves II
by Joseph H Silverman
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2 editions published in 1994 in English and held by 8 WorldCat member libraries worldwide
Hajimete no sūron : Hakken to shōmei no daikōkai  pitagorasu no teiri kara daen kyokusen made
by Joseph H Silverman
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5 editions published between 2001 and 2014 in Japanese and held by 5 WorldCat member libraries worldwide
Daen kyokusenron nyūmon
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3 editions published between 1995 and 2012 in Japanese and held by 3 WorldCat member libraries worldwide
Folk literature of the Sephardic Jews
by Samuel G Armistead
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in English and held by 3 WorldCat member libraries worldwide
Modular Forms and Fermat's Last Theorem : Papers from a Conference on Number Theory and Arithmetic Geometry, August 918, 1995, at Boston University, USA
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Book
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1 edition published in 1997 in English and held by 3 WorldCat member libraries worldwide
LOW FREQUENCY GYRATOR DEVELOPMENT
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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
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Book
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3 editions published in 2003 in Japanese and held by 2 WorldCat member libraries worldwide
Daen kyokusen ron gaisetsu
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3 editions published in 2003 in Japanese and held by 2 WorldCat member libraries worldwide more
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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) Differentiable dynamical systems Diophantine analysis Diophantine equations Dynamics Ergodic theory Fermat's last theorem Fermat's theorem Folk literature, Ladino Forms, Modular Fundamental theorem of algebra Geometry Geometry, Algebraic Geometry of numbers Harmonic analysis Irrational numbers Lattice theory Mathematics Moduli theory Number theory Partitions (Mathematics) Quadratic fields Rational points (Geometry) Series Signs and symbols

Alternative Names
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.
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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