Rational Points on Curves Over Finite Fields

Theory and Applications

Author: Harald Niederreiter,Chaoping Xing

Publisher: Cambridge University Press

ISBN: 9780521665438

Category: Mathematics

Page: 245

View: 5406

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Discussion of theory and applications of algebraic curves over finite fields with many rational points.

Finite Fields and Applications

7th International Conference, Fq7, Toulouse, France, May 5-9, 2003, Revised Papers

Author: Gary L. Mullen,Alain Poli,Henning Stichtenoth

Publisher: Springer

ISBN: 3540246339

Category: Mathematics

Page: 263

View: 2959

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Algebraic Curves Over a Finite Field

Author: James William Peter Hirschfeld,G. Korchmáros,F. Torres

Publisher: Princeton University Press

ISBN: 9780691096797

Category: Mathematics

Page: 696

View: 824

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This title provides a self-contained introduction to the theory of algebraic curves over a finite field, whose origins can be traced back to the works of Gauss and Galois on algebraic equations in two variables with coefficients modulo a prime number.

Algebraic Curves and Finite Fields

Cryptography and Other Applications

Author: Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110379554

Category: Mathematics

Page: 251

View: 1663

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This book collects the results of the workshops on Applications of Algebraic Curves and Applications of Finite Fields at the RICAM in 2013. These workshops brought together the most prominet researchers in the area of finite fields and their applications around the world, addressing old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Encyclopedia of Statistical Sciences

Author: Samuel Kotz

Publisher: Wiley-Interscience

ISBN: 9780471743767

Category: Mathematics

Page: 680

View: 4045

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Countless professionals and students who use statistics in their work rely on the multi-volume Encyclopedia of Statistical Sciences as a superior and unique source of information on statistical theory, methods, and applications. This new edition (available in both print and on-line versions) is designed to bring the encyclopedia in line with the latest topics and advances made in statistical science over the past decade--in areas such as computer-intensive statistical methodology, genetics, medicine, the environment, and other applications. Written by over 600 world-renowned experts (including the editors), the entries are self-contained and easily understood by readers with a limited statistical background. With the publication of this second edition in 16 printed volumes, the Encyclopedia of Statistical Sciences retains its position as a cutting-edge reference of choice for those working in statistics, biostatistics, quality control, economics, sociology, engineering, probability theory, computer science, biomedicine, psychology, and many other areas. The Encyclopedia of Statistical Sciences is also available as a 16 volume A to Z set. Volume 6: In-L.

L-Functions and Galois Representations

Author: David Burns,Kevin Buzzard,Jan Nekovář

Publisher: Cambridge University Press

ISBN: 0521694159

Category: Mathematics

Page: 563

View: 1076

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This collection of survey and research articles brings together topics at the forefront of the theory of L-functions and Galois representations. Highlighting important progress in areas such as the local Langlands programme, automorphic forms and Selmer groups, this timely volume treats some of the most exciting recent developments in the field. Included are survey articles from Khare on Serre's conjecture, Yafaev on the André-Oort conjecture, Emerton on his theory of Jacquet functors, Venjakob on non-commutative Iwasawa theory and Vigneras on mod p representations of GL(2) over p-adic fields. There are also research articles by: Böckle, Buzzard, Cornut and Vatsal, Diamond, Hida, Kurihara and R. Pollack, Kisin, Nekovář, and Bertolini, Darmon and Dasgupta. Presenting the very latest research on L-functions and Galois representations, this volume is indispensable for researchers in algebraic number theory.

Rational Points on Elliptic Curves

Author: Joseph H. Silverman,John T. Tate

Publisher: Springer

ISBN: 3319185888

Category: Mathematics

Page: 332

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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.

Elliptic Curves in Cryptography

Author: I. Blake,G. Seroussi,N. Smart

Publisher: Cambridge University Press

ISBN: 9780521653749

Category: Computers

Page: 204

View: 7699

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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.

Sheaves and Functions Modulo p

Lectures on the Woods Hole Trace Formula

Author: Lenny Taelman

Publisher: Cambridge University Press

ISBN: 1316571793

Category: Mathematics

Page: N.A

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The Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Böckle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta values.

Reversibility in Dynamics and Group Theory

Author: Anthony G. O'Farrell,Ian Short

Publisher: Cambridge University Press

ISBN: 1107442885

Category: Mathematics

Page: 292

View: 6526

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An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

Algebraic Curves Over Finite Fields

Author: Carlos Moreno

Publisher: Cambridge University Press

ISBN: 9780521459013

Category: Mathematics

Page: 260

View: 4353

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Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.

Advances in Elliptic Curve Cryptography

Author: Ian F. Blake,Gadiel Seroussi,Nigel P. Smart

Publisher: Cambridge University Press

ISBN: 9781139441223

Category: Mathematics

Page: N.A

View: 974

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Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.

Surveys in Combinatorics 2003

Author: C. D. Wensley

Publisher: Cambridge University Press

ISBN: 9780521540124

Category: Mathematics

Page: 378

View: 3351

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The British Combinatorial Conference attracts a large following from the U.K. and international research community. Held at the University of Wales, Bangor, in 2003, the speakers included renowned experts on topics currently attracting significant research interest, as well as less traditional areas such as the combinatorics of protecting digital content. All the contributions are survey papers presenting an overview of the state of the art in a particular area.

Arithmetic and Geometry

Author: Luis Dieulefait,Gerd Faltings,D. R. Heath-Brown,Yuri I. Manin,B. Z. Moroz,Yu. V. Manin,Jean-Pierre Wintenberger

Publisher: Cambridge University Press

ISBN: 1107462541

Category: Mathematics

Page: 550

View: 1032

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The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

The Arithmetic of Elliptic Curves

Author: Joseph H. Silverman

Publisher: Springer Science & Business Media

ISBN: 1475719205

Category: Mathematics

Page: 402

View: 7493

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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 approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Anthony Hilton,John Talbot

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 2500

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