Elementary And Analytic Theory Of Algebraic Numbers
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Elementary And Analytic Theory Of Algebraic Numbers
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-24
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 2004-06-24 with Mathematics categories.
This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.
Elementary And Analytic Theory Of Algebraic Numbers
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Author : Wadysaw Narkiewicz
language : en
Publisher:
Release Date : 2014-01-15
Elementary And Analytic Theory Of Algebraic Numbers written by Wadysaw Narkiewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Elementary And Analytic Theory Of Algebraic Numbers
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Author : Wladyslaw Narkiewicz
language : en
Publisher:
Release Date : 1985
Elementary And Analytic Theory Of Algebraic Numbers written by Wladyslaw Narkiewicz 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.
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.
Elementary Analytic Theory Of Algebraic Numbers
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Author : Władysław Narkiewicz
language : de
Publisher:
Release Date : 1974
Elementary Analytic Theory Of Algebraic Numbers written by Władysław Narkiewicz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Classical Theory Of Algebraic Numbers
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Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Classical Theory Of Algebraic Numbers written by Paulo Ribenboim 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.
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem. These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others. This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography. This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples. The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields. Part One is devoted to residue classes and quadratic residues. In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals. Part Three is devoted to Kummer's theory of cyclomatic fields, and includes Bernoulli numbers and the proof of Fermat's Last Theorem for regular prime exponents. Finally, in Part Four, the emphasis is on analytical methods and it includes Dinchlet's Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas. A careful study of this book will provide a solid background to the learning of more recent topics.
Algebraic Number Theory And Diophantine Analysis
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Author : F. Halter-Koch
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Algebraic Number Theory And Diophantine Analysis written by F. Halter-Koch 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 2011-06-24 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
An Invitation To Algebraic Numbers And Algebraic Functions
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Author : Franz Halter-Koch
language : en
Publisher: CRC Press
Release Date : 2020-05-18
An Invitation To Algebraic Numbers And Algebraic Functions written by Franz Halter-Koch and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-18 with Mathematics categories.
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
The Story Of Algebraic Numbers In The First Half Of The 20th Century
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Author : Władysław Narkiewicz
language : en
Publisher: Springer
Release Date : 2019-01-18
The Story Of Algebraic Numbers In The First Half Of The 20th Century written by Władysław Narkiewicz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-18 with Mathematics categories.
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
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"