Theory Of Algebraic Integers
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The Theory Of Algebraic Numbers Second Edition
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Author : Harry Pollard
language : en
Publisher: American Mathematical Soc.
Release Date : 1975-12-31
The Theory Of Algebraic Numbers Second Edition written by Harry Pollard 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 1975-12-31 with Algebraic number theory categories.
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Theory Of Algebraic Integers
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Author : Richard Dedekind
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-28
Theory Of Algebraic Integers written by Richard Dedekind 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 1996-09-28 with Mathematics categories.
A translation of a classic work by one of the truly great figures of mathematics.
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.
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.
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.
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
The Theory Of Algebraic Numbers
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Author : Harry Pollard
language : en
Publisher:
Release Date : 1961
The Theory Of Algebraic Numbers written by Harry Pollard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Algebraic fields categories.
Number Theory
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Author : Helmut Koch
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Number Theory written by Helmut Koch 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 2000 with Mathematics categories.
Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Lectures On The Theory Of Algebraic Numbers
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Author : E. T. Hecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Lectures On The Theory Of Algebraic Numbers written by E. T. Hecke 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.
. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
Number Theory
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Author : W Narkiewicz
language : en
Publisher: World Scientific Publishing Company
Release Date : 1984-02-01
Number Theory written by W Narkiewicz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-02-01 with Mathematics categories.
The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.
Elementary And Analytic Theory Of Algebraic Numbers
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Author : Władysław Narkiewicz
language : en
Publisher: Springer Verlag
Release Date : 1990
Elementary And Analytic Theory Of Algebraic Numbers written by Władysław Narkiewicz and has been published by Springer Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Algebraic number theory categories.
Algebraic Number Theory And Fermat S Last Theorem
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Author : Ian Stewart
language : en
Publisher: CRC Press
Release Date : 2015-10-14
Algebraic Number Theory And Fermat S Last Theorem written by Ian Stewart and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Mathematics categories.
Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fourth Edition Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(√14) is Euclidean Presents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844 Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last Theorem Improves and updates the index, figures, bibliography, further reading list, and historical remarks Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.