Rational Points On Curves Over Finite Fields
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Rational Points On Curves Over Finite Fields
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Author : Harald Niederreiter
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-14
Rational Points On Curves Over Finite Fields written by Harald Niederreiter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-14 with Computers categories.
Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Rational Points On Curves Over Finite Fields
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Author : Søren Have Hansen
language : en
Publisher:
Release Date : 1995
Rational Points On Curves Over Finite Fields written by Søren Have Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Curves, Algebraic categories.
Rational Points On Curves Over Finite Fields
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Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 2020
Rational Points On Curves Over Finite Fields written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
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.
Algebraic Curves Over A Finite Field
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Author : J. W. P. Hirschfeld
language : en
Publisher: Princeton University Press
Release Date : 2013-03-25
Algebraic Curves Over A Finite Field written by J. W. P. Hirschfeld and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Mathematics categories.
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.
Rational Points On Curves Over Finite Fields
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Author : Jean-Pierre Serre
language : en
Publisher:
Release Date : 1985
Rational Points On Curves Over Finite Fields written by Jean-Pierre Serre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Applications Of Curves Over Finite Fields
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Author : Michael D. Fried
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Applications Of Curves Over Finite Fields written by Michael D. Fried and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following: 1. Curves with many rational points. Several articles describe main approaches to the construction of such curves: the Drinfeld modules and fiber product methods, the moduli space approach, and the constructions using classical curves. 2. Monodromy groups of characteristic $p$ covers. A number of authors presented the results and conjectures related to the study of the monodromy groups of curves over finite fields. In particular, they study the monodromy groups from genus 0 covers, reductions of covers, and explicit computation of monodromy groups over finite fields. 3. Zeta functions and trace formulas. To a large extent, papers devoted to this topic reflect the contributions of Professor Bernard Dwork and his students. This conference was the last attended by Professor Dwork before his death, and several papers inspired by his presence include commentaries about the applications of trace formulas and L-function. The volume also contains a detailed introduction paper by Professor Michael Fried, which helps the reader to navigate the material presented in the book.
Rational Points On Elliptic Curves
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Author : Joseph H. Silverman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Rational Points On Elliptic Curves written by Joseph H. Silverman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Higher Dimensional Geometry Over Finite Fields
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Author : D. Kaledin
language : en
Publisher: IOS Press
Release Date : 2008-06-05
Higher Dimensional Geometry Over Finite Fields written by D. Kaledin and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-05 with Mathematics categories.
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields. The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.
Codes On Algebraic Curves
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Author : Serguei A. Stepanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Codes On Algebraic Curves written by Serguei A. Stepanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
Many Rational Points
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Author : N.E. Hurt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Many Rational Points written by N.E. Hurt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators." "The book will be of use to mathematicians, physicists and engineers interested in the mathematical methods of algebraic geometry as they apply to coding theory and cryptography."--Jacket