Rational Points on Curves Over Finite Fields PDF Download
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Author: Harald Niederreiter
Publisher: Cambridge University Press
ISBN: 9780521665438
Category : Computers
Languages : en
Pages : 260
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Book Description
Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Author: Harald Niederreiter
Publisher: Cambridge University Press
ISBN: 9780521665438
Category : Computers
Languages : en
Pages : 260
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Book Description
Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Author: Jean-Pierre Serre
Publisher:
ISBN: 9782856299234
Category :
Languages : en
Pages : 187
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Book Description
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
Publisher: Springer Science & Business Media
ISBN: 1475742525
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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
Publisher:
ISBN:
Category : Curves, Algebraic
Languages : en
Pages : 92
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Book Description
Author: J. W. P. Hirschfeld
Publisher: Princeton University Press
ISBN: 1400847419
Category : Mathematics
Languages : en
Pages : 717
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Jean-Pierre Serre
Publisher:
ISBN:
Category :
Languages : en
Pages : 132
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Book Description
Author: Jean-Pierre Serre
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Robert Rolland
Publisher: World Scientific
ISBN: 9814471666
Category : Mathematics
Languages : en
Pages : 530
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Book Description
This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Author: Carlos Moreno
Publisher: Cambridge University Press
ISBN: 9780521459013
Category : Mathematics
Languages : en
Pages : 264
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Book Description
Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
