Background
Silverman, Joseph Hillel was born on March 27, 1955 in New York City. Son of Harry and Shirley (Seiner) Silverman.
(The theory of elliptic curves is distinguished by its lon...)
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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
http://www.amazon.com/gp/product/0387094938/?tag=2022091-20
(In the introduction to the first volume of The Arithmetic...)
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
http://www.amazon.com/gp/product/0387943285/?tag=2022091-20
( The theory of elliptic curves involves a blend of algeb...)
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
http://www.amazon.com/gp/product/0387978259/?tag=2022091-20
( The theory of elliptic curves involves a pleasing blend...)
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume 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 Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel 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.
http://www.amazon.com/gp/product/331918587X/?tag=2022091-20
(In the introduction to the first volume of The Arithmetic...)
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
http://www.amazon.com/gp/product/0387943285/?tag=2022091-20
( This is an introduction to diophantine geometry at the ...)
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
http://www.amazon.com/gp/product/0387989811/?tag=2022091-20
( This book provides an introduction to the relatively ne...)
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic 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.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
http://www.amazon.com/gp/product/0387699031/?tag=2022091-20
( This book provides an introduction to the relatively ne...)
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic 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.This graduate-level text provides an entry for students into an active field of research and serves as a standard reference for researchers.
http://www.amazon.com/gp/product/1441924175/?tag=2022091-20
Silverman, Joseph Hillel was born on March 27, 1955 in New York City. Son of Harry and Shirley (Seiner) Silverman.
Standard Chartered Bank, Brown University, 1977. Master of Arts, Harvard University, 1979. Doctor of Philosophy, Harvard University, 1982.
Moore instructor Massachusetts Institute of Technology, Cambridge, 1982-1986. Associate professor Boston University, 1986-1988. Associate professor mathematics Brown University, Providence, 1988-1991, professor, since 1991, chairman, 2001—2004.
Founder and vice president research, NTRU Cryptosystems, Inc., 1997—2009.
(In the introduction to the first volume of The Arithmetic...)
(In the introduction to the first volume of The Arithmetic...)
(The theory of elliptic curves is distinguished by its lon...)
( The theory of elliptic curves involves a pleasing blend...)
( The theory of elliptic curves involves a blend of algeb...)
( This book provides an introduction to the relatively ne...)
( This book provides an introduction to the relatively ne...)
( This is an introduction to diophantine geometry at the ...)
("This is the International Edition. The content is in Eng...)
(the one and only)
Member American Mathematics Society (Steele prize 1998).
Married Susan Leslie Greenhaus, June 13, 1976. Children: Deborah, Daniel, Jonathan.