The Theory Of Algebraic Number Fields

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The Theory of Algebraic Number Fields

David Hilbert
The Theory of Algebraic Number Fields Book PDF

Author : David Hilbert
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 41,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662035450

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The Theory of Algebraic Number Fields by David Hilbert Pdf

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.

Algebraic Number Fields

Gerald J. Janusz
Algebraic Number Fields Book PDF

Author : Gerald J. Janusz
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 50,5 Mb
Release : 1996
Category : Algebraic fields
ISBN : 9780821804292

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Algebraic Number Fields by Gerald J. Janusz Pdf

This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.

The Theory of Algebraic Numbers: Second Edition

Harry Pollard,Harold G. Diamond
The Theory of Algebraic Numbers Second Edition Book PDF

Author : Harry Pollard,Harold G. Diamond
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 53,9 Mb
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 9781614440093

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The Theory of Algebraic Numbers: Second Edition by Harry Pollard,Harold G. Diamond Pdf

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.

Number Fields

Daniel A. Marcus
Number Fields Book PDF

Author : Daniel A. Marcus
Publisher : Springer
Page : 203 pages
File Size : 54,8 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319902333

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Number Fields by Daniel A. Marcus Pdf

Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.

A Brief Guide to Algebraic Number Theory

H. P. F. Swinnerton-Dyer
A Brief Guide to Algebraic Number Theory Book PDF

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 46,5 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Classical Theory of Algebraic Numbers

Paulo Ribenboim
Classical Theory of Algebraic Numbers Book PDF

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 54,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387216904

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Classical Theory of Algebraic Numbers by Paulo Ribenboim Pdf

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.

Lectures on the Theory of Algebraic Numbers

E. T. Hecke
Lectures on the Theory of Algebraic Numbers Book PDF

Author : E. T. Hecke
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 42,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740929

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Lectures on the Theory of Algebraic Numbers by E. T. Hecke Pdf

. . . 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.

A Classical Invitation to Algebraic Numbers and Class Fields

Harvey Cohn
A Classical Invitation to Algebraic Numbers and Class Fields Book PDF

Author : Harvey Cohn
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299509

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A Classical Invitation to Algebraic Numbers and Class Fields by Harvey Cohn Pdf

"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"

Algebraic Number Theory

Edwin Weiss
Algebraic Number Theory Book PDF

Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 40,9 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154367

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Algebraic Number Theory by Edwin Weiss Pdf

Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Algebraic Number Theory

Frazer Jarvis
Algebraic Number Theory Book PDF

Author : Frazer Jarvis
Publisher : Springer
Page : 292 pages
File Size : 44,7 Mb
Release : 2014-06-23
Category : Mathematics
ISBN : 9783319075457

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Algebraic Number Theory by Frazer Jarvis Pdf

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

Algebraic Number Theory and Fermat's Last Theorem

Ian Stewart,David Tall
Algebraic Number Theory and Fermat s Last Theorem Book PDF

Author : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 44,7 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081

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Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart,David Tall Pdf

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

The Genus Fields of Algebraic Number Fields

M. Ishida
The Genus Fields of Algebraic Number Fields Book PDF

Author : M. Ishida
Publisher : Springer
Page : 123 pages
File Size : 49,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540375531

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The Genus Fields of Algebraic Number Fields by M. Ishida Pdf

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Number Theory in Function Fields

Michael Rosen
Number Theory in Function Fields Book PDF

Author : Michael Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 55,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781475760460

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Number Theory in Function Fields by Michael Rosen Pdf

Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

Cohomology of Number Fields

Jürgen Neukirch,Alexander Schmidt,Kay Wingberg
Cohomology of Number Fields Book PDF

Author : Jürgen Neukirch,Alexander Schmidt,Kay Wingberg
Publisher : Springer Science & Business Media
Page : 831 pages
File Size : 52,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9783540378891

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Cohomology of Number Fields by Jürgen Neukirch,Alexander Schmidt,Kay Wingberg Pdf

This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.

Algebraic Number Theory

H. Koch
Algebraic Number Theory Book PDF

Author : H. Koch
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580956

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Algebraic Number Theory by H. Koch Pdf

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995