Numerical Algorithms For Number Theory Using Pari Gp

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Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas,Henri Cohen
Numerical Algorithms for Number Theory Using Pari GP Book PDF

Author : Karim Belabas,Henri Cohen
Publisher : American Mathematical Soc.
Page : 429 pages
File Size : 42,8 Mb
Release : 2021-06-23
Category : Education
ISBN : 9781470463519

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Numerical Algorithms for Number Theory: Using Pari/GP by Karim Belabas,Henri Cohen Pdf

This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.

Applications of Number Theory to Numerical Analysis

L.-K. Hua,Y. Wang
Applications of Number Theory to Numerical Analysis Book PDF

Author : L.-K. Hua,Y. Wang
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642678295

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Applications of Number Theory to Numerical Analysis by L.-K. Hua,Y. Wang Pdf

Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions.

Arithmetic of Finite Fields

Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc
Arithmetic of Finite Fields Book PDF

Author : Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc
Publisher : Springer
Page : 205 pages
File Size : 47,7 Mb
Release : 2008-07-08
Category : Computers
ISBN : 9783540694991

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Arithmetic of Finite Fields by Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc Pdf

This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.

A Course in Computational Algebraic Number Theory

Henri Cohen
A Course in Computational Algebraic Number Theory Book PDF

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 48,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Elementary Number Theory: Primes, Congruences, and Secrets

William Stein
Elementary Number Theory Primes Congruences and Secrets Book PDF

Author : William Stein
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 43,5 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9780387855257

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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Pdf

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Mathematics Going Forward

Jean-Michel Morel,Bernard Teissier
Mathematics Going Forward Book PDF

Author : Jean-Michel Morel,Bernard Teissier
Publisher : Springer Nature
Page : 629 pages
File Size : 44,5 Mb
Release : 2023-06-14
Category : Mathematics
ISBN : 9783031122446

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Mathematics Going Forward by Jean-Michel Morel,Bernard Teissier Pdf

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Unsolved Problems in Number Theory

Richard Guy
Unsolved Problems in Number Theory Book PDF

Author : Richard Guy
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 42,7 Mb
Release : 2004-07-13
Category : Mathematics
ISBN : 0387208607

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Unsolved Problems in Number Theory by Richard Guy Pdf

Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

A Course in Number Theory and Cryptography

Neal Koblitz
A Course in Number Theory and Cryptography Book PDF

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 40,5 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Computational Number Theory

Abhijit Das
Computational Number Theory Book PDF

Author : Abhijit Das
Publisher : CRC Press
Page : 614 pages
File Size : 42,6 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781482205824

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Computational Number Theory by Abhijit Das Pdf

Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract

Algorithmic Number Theory: Efficient algorithms

Eric Bach,Jeffrey Outlaw Shallit
Algorithmic Number Theory Efficient algorithms Book PDF

Author : Eric Bach,Jeffrey Outlaw Shallit
Publisher : MIT Press
Page : 536 pages
File Size : 55,9 Mb
Release : 1996
Category : Computers
ISBN : 0262024055

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Algorithmic Number Theory: Efficient algorithms by Eric Bach,Jeffrey Outlaw Shallit Pdf

Volume 1.

Progress in Cryptology -- AFRICACRYPT 2012

Aikaterini Mitrokotsa,Serge Vaudenay
Progress in Cryptology AFRICACRYPT 2012 Book PDF

Author : Aikaterini Mitrokotsa,Serge Vaudenay
Publisher : Springer
Page : 424 pages
File Size : 43,6 Mb
Release : 2012-06-21
Category : Computers
ISBN : 9783642314100

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Progress in Cryptology -- AFRICACRYPT 2012 by Aikaterini Mitrokotsa,Serge Vaudenay Pdf

This book constitutes the refereed proceedings of the 5th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2011, held in Ifrane, Morocco, in July 2012. The 24 papers presented together with abstracts of 2 invited talks were carefully reviewed and selected from 56 submissions. They are organized in topical sections on signature schemes, stream ciphers, applications of information theory, block ciphers, network security protocols, public-key cryptography, cryptanalysis of hash functions, hash functions: design and implementation, algorithms for public-key cryptography, and cryptographic protocols.

Experimental Number Theory

Fernando Rodriguez Villegas
Experimental Number Theory Book PDF

Author : Fernando Rodriguez Villegas
Publisher : OUP Oxford
Page : 232 pages
File Size : 46,8 Mb
Release : 2007-05-24
Category : Mathematics
ISBN : 9780191523731

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Experimental Number Theory by Fernando Rodriguez Villegas Pdf

This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website.

LuCaNT: LMFDB, Computation, and Number Theory

John Cremona,John Jones,Jennifer Paulhus,Andrew V. Sutherlan,John Voight
LuCaNT LMFDB Computation and Number Theory Book PDF

Author : John Cremona,John Jones,Jennifer Paulhus,Andrew V. Sutherlan,John Voight
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 52,9 Mb
Release : 2024-03-22
Category : Mathematics
ISBN : 9781470472603

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LuCaNT: LMFDB, Computation, and Number Theory by John Cremona,John Jones,Jennifer Paulhus,Andrew V. Sutherlan,John Voight Pdf

This book will be published Open Access with a Creative Commons Attribution 4.0 International License (CC BY 4.0). The eBook can be downloaded electronically for free. This volume contains the proceedings of the LuCaNT (LMFDB, Computation, and Number Theory) conference held from July 10–14, 2023, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island and affiliated with Brown University. This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFDB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.

Number Theory for Computing

Song Y. Yan
Number Theory for Computing Book PDF

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 46,8 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783662047736

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Number Theory for Computing by Song Y. Yan Pdf

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

Number Theory

Wenpeng Zhang,Yoshio Tanigawa
Number Theory Book PDF

Author : Wenpeng Zhang,Yoshio Tanigawa
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 44,6 Mb
Release : 2006-06-05
Category : Mathematics
ISBN : 9780387308296

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Number Theory by Wenpeng Zhang,Yoshio Tanigawa Pdf

This book collects survey and research papers on various topics in number theory. Although the topics and descriptive details appear varied, they are unified by two underlying principles: first, readability, and second, a smooth transition from traditional approaches to modern ones. Thus, on one hand, the traditional approach is presented in great detail, and on the other, the modernization of the methods in number theory is elaborated.