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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…mehr

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Produktbeschreibung
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.

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Autorenporträt
Dr. Joseph Silverman is a professor at Brown University and has been an instructor or professors since 1982. He was the Chair of the Brown Mathematics department from 2001-2004. He has received numerous fellowships, grants and awards, as well as being a frequently invited lecturer. He is currently a member of the Council of the American Mathematical Society. His research areas of interest are number theory, arithmetic geometry, elliptic curves, dynamical systems and cryptography. He has co-authored over 120 publications and has had over 20 doctoral students under his tutelage. He has published 9 highly successful books with Springer, including the recently released, An Introduction to Mathematical Cryptography, for Undergraduate Texts in Mathematics.