Computational Problems Methods And Results In Algebraic Number Theory
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Computational Problems Methods And Results In Algebraic Number Theory
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Author : H. G. Zimmer
language : en
Publisher: Springer
Release Date : 2006-11-15
Computational Problems Methods And Results In Algebraic Number Theory written by H. G. Zimmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Computational Problems Methods And Results In Algebraic Number Theory
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Author : Horst G. Zimmer
language : en
Publisher: Springer
Release Date : 1972-01-01
Computational Problems Methods And Results In Algebraic Number Theory written by Horst G. Zimmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-01 with Algebraic number theory categories.
A Course In Computational Algebraic Number Theory
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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Course In Computational Algebraic Number Theory written by Henri Cohen 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.
With the advent of powerful computing tools and numerous advances in math ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
Algorithmic Algebraic Number Theory
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Author : M. Pohst
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-25
Algorithmic Algebraic Number Theory written by M. Pohst 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 1997-09-25 with Mathematics categories.
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
The Development Of The Number Field Sieve
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Author : Arjen K. Lenstra
language : en
Publisher: Springer
Release Date : 2006-11-15
The Development Of The Number Field Sieve written by Arjen K. Lenstra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Elementary And Analytic Theory Of Algebraic Numbers
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Elementary And Analytic Theory Of Algebraic Numbers written by Wladyslaw Narkiewicz 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 2013-06-29 with Mathematics categories.
The aim of this book is to present an exposition of the theory of alge braic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numeri cal computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis. Thus the author has tried to reconcile the two approaches, presenting a self-contained exposition of the classical standpoint in the first four chapters, and then turning to local methods. In the first chapter we present the necessary tools from the theory of Dedekind domains and valuation theory, including the structure of finitely generated modules over Dedekind domains. In Chapters 2, 3 and 4 the clas sical theory of algebraic numbers is developed. Chapter 5 contains the fun damental notions of the theory of p-adic fields, and Chapter 6 brings their applications to the study of algebraic number fields. We include here Shafare vich's proof of the Kronecker-Weber theorem, and also the main properties of adeles and ideles.
Computational And Algorithmic Problems In Finite Fields
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Author : Igor Shparlinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational And Algorithmic Problems In Finite Fields 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 2012-12-06 with Mathematics categories.
This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, 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 araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
A Classical Invitation To Algebraic Numbers And Class Fields
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Author : Harvey Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Classical Invitation To Algebraic Numbers And Class Fields written by Harvey Cohn 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.
"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Ordinary And Partial Differential Equations
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Author : B.D. Sleeman
language : en
Publisher: Springer
Release Date : 2006-11-15
Ordinary And Partial Differential Equations written by B.D. Sleeman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Hypoellipticity And Eigenvalue Asymptotics
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Author : C. Rockland
language : en
Publisher: Springer
Release Date : 2006-11-14
Hypoellipticity And Eigenvalue Asymptotics written by C. Rockland and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.