The Arithmetic of Elliptic Curves
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Home > Mathematics and Science Textbooks > Mathematics > Geometry > Algebraic geometry > The Arithmetic of Elliptic Curves: (106 Graduate Texts in Mathematics)
The Arithmetic of Elliptic Curves: (106 Graduate Texts in Mathematics)

The Arithmetic of Elliptic Curves: (106 Graduate Texts in Mathematics)


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About the Book

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 algebro-geometric 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.

Table of Contents:
Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of an Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell#x2013;Weil Group.- Algorithmic Aspects of Elliptic Curves.

About the Author :
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.

Review :
From the reviews of the second edition: "This well-written book covers the basic facts about the geometry and arithmetic of elliptic curves, and is sure to become the standard reference in the subject. It meets the needs of at least three groups of people: students interested in doing research in Diophantine geometry, mathematicians needing a reference for standard facts about elliptic curves, and computer scientists interested in algorithms and needing an introduction to elliptic curves..."-- MATHEMATICAL REVIEWS "The book under review is the second, revised, enlarged, and updated edition of J. Silverman,s meanwhile classical primer of the arithmetic of elliptic curves. ... All together, this enlarged and updated version of J. Silverman,s classic 'The Arithmetic of Elliptic Curves, significantly increases the unchallenged value of this modern primer as a standard textbook in the field. ... This makes the entire text a perfect source for teachers and students, for courses and self-study, and for further studies in the arithmetic of elliptic curves likewise." (Werner Kleinert, Zentralblatt MATH, Vol. 1194, 2010) "For the second edition of his masterly book, the author considerably updated and improved several results and proofs. ... book contains a great many exercises, many of which develop or complement the results from the main body of the book. ... The reference list contains 317 items and reflects both classical and recent achievements on the topic. Notes on the exercises are an aid to the reader. ... Summarizing, this is an excellent book ... . useful both for experienced mathematicians and for graduate students." (Vasil' I. Andriichuk, Mathematical Reviews, Issue 2010 i) "This is the second edition of an excellent textbook on the arithmetical theory of elliptic curves ... . Although there are now a number of good books on this topic it has stood the test of time and become a popular introductory text and a standard reference. ... The author has added remarks which point out their significance and connection to those parts of the theory he presents. These will give readers a good start if they want to study one of them." (Ch. Baxa, Monatshefte fur Mathematik, Vol. 164 (3), November, 2011)


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Product Details
  • ISBN-13: 9781441918581
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Edition: Revised edition
  • Language: English
  • Returnable: N
  • Series Title: 106 Graduate Texts in Mathematics
  • ISBN-10: 1441918582
  • Publisher Date: 19 Nov 2010
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 513
  • Returnable: N
  • Width: 155 mm


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