Rational Points On Elliptic Curves Over Finite Fields
DOWNLOAD
Download Rational Points On Elliptic Curves Over Finite Fields PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Rational Points On Elliptic Curves Over Finite Fields book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Rational Points On Elliptic Curves Over Finite Fields
DOWNLOAD
Author : 黃柏嶧
language : en
Publisher:
Release Date : 1999
Rational Points On Elliptic Curves Over Finite Fields written by 黃柏嶧 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Distribution Of The Number Of Rational Points On Elliptic Curves Over Finite Fields
DOWNLOAD
Author : Vita Pasic
language : en
Publisher:
Release Date : 2009
Distribution Of The Number Of Rational Points On Elliptic Curves Over Finite Fields written by Vita Pasic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Rational Points On Elliptic Curves
DOWNLOAD
Author : Joseph H. Silverman
language : en
Publisher: Springer
Release Date : 2015-06-02
Rational Points On Elliptic Curves written by Joseph H. Silverman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-02 with Mathematics categories.
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Finite Fields Theory And Computation
DOWNLOAD
Author : Igor Shparlinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Finite Fields Theory And Computation written by Igor Shparlinski 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 2013-03-09 with Mathematics categories.
This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Elliptic Curves
DOWNLOAD
Author : Dale Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-06
Elliptic Curves written by Dale Husemöller 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 2006-06-06 with Mathematics categories.
There are three new appendices, one by Stefan Theisen on the role of Calabi– Yau manifolds in string theory and one by Otto Forster on the use of elliptic curves in computing theory and coding theory. In the third appendix we discuss the role of elliptic curves in homotopy theory. In these three introductions the reader can get a clue to the far-reaching implications of the theory of elliptic curves in mathematical sciences. During the ?nal production of this edition, the ICM 2002 manuscript of Mike Hopkins became available. This report outlines the role of elliptic curves in ho- topy theory. Elliptic curves appear in the form of the Weierstasse equation and its related changes of variable. The equations and the changes of variable are coded in an algebraic structure called a Hopf algebroid, and this Hopf algebroid is related to a cohomology theory called topological modular forms. Hopkins and his coworkers have used this theory in several directions, one being the explanation of elements in stable homotopy up to degree 60. In the third appendix we explain how what we described in Chapter 3 leads to the Weierstrass Hopf algebroid making a link with Hopkins’ paper.
Algebraic Curves Over A Finite Field
DOWNLOAD
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.
Elliptic Curves
DOWNLOAD
Author : Susanne Schmitt
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Elliptic Curves written by Susanne Schmitt and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.
Elliptic Curves And Their Arithmetic Geometry
DOWNLOAD
Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-07-28
Elliptic Curves And Their Arithmetic Geometry written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-28 with Mathematics categories.
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
Elliptic Curves In Cryptography
DOWNLOAD
Author : Ian F. Blake
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-08
Elliptic Curves In Cryptography written by Ian F. Blake 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 1999-07-08 with Computers categories.
This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.
Applications Of Curves Over Finite Fields
DOWNLOAD
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.