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Author : Harald Niederreiter
Release : 2001-06-14
Genre : Computers
Kind : eBook
Book Rating : 438/5 ( reviews)
Book Synopsis Rational Points on Curves Over Finite Fields by : Harald Niederreiter
Download or read book Rational Points on Curves Over Finite Fields written by Harald Niederreiter. This book was released on 2001-06-14. Available in PDF, EPUB and Kindle. Book excerpt: Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Author : Jean-Pierre Serre
Release : 2020
Genre :
Kind : eBook
Book Rating : 234/5 ( reviews)
Book Synopsis Rational Points on Curves Over Finite Fields by : Jean-Pierre Serre
Download or read book Rational Points on Curves Over Finite Fields written by Jean-Pierre Serre. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt: In 1985 Jean-Pierre Serre gave a series of lectures at Harvard University on the number of points of curves over finite fields. Based on notes taken at that time by F. Q. Gouvea, the present revised and completed documents provides an insightful introduction to this beautiful topic and to most of the ideas that have been developed in this area during the last 30 years.
Author : Joseph H. Silverman
Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 525/5 ( reviews)
Book Synopsis Rational Points on Elliptic Curves by : Joseph H. Silverman
Download or read book Rational Points on Elliptic Curves written by Joseph H. Silverman. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Søren Have Hansen
Release : 1995
Genre : Curves, Algebraic
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Rational Points on Curves Over Finite Fields by : Søren Have Hansen
Download or read book Rational Points on Curves Over Finite Fields written by Søren Have Hansen. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. W. P. Hirschfeld
Release : 2013-03-25
Genre : Mathematics
Kind : eBook
Book Rating : 419/5 ( reviews)
Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld
Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld. This book was released on 2013-03-25. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
