The Theory of Algebraic Numbers: Second Edition PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Theory of Algebraic Numbers: Second Edition PDF full book. Access full book title The Theory of Algebraic Numbers: Second Edition by Harry Pollard. Download full books in PDF and EPUB format.
Author: Harry Pollard
Publisher: American Mathematical Soc.
ISBN: 1614440093
Category : Mathematics
Languages : en
Pages : 175
Get Book Here
Book Description
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.
Author: Harry Pollard
Publisher: American Mathematical Soc.
ISBN: 1614440093
Category : Mathematics
Languages : en
Pages : 175
Get Book Here
Book Description
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.
Author: Paulo Ribenboim
Publisher: Springer Science & Business Media
ISBN: 0387216901
Category : Mathematics
Languages : en
Pages : 676
Get Book Here
Book Description
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.
Author: Helmut Koch
Publisher: American Mathematical Soc.
ISBN: 9780821820544
Category : Mathematics
Languages : en
Pages : 390
Get Book Here
Book Description
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.
Author: E. T. Hecke
Publisher: Springer Science & Business Media
ISBN: 1475740921
Category : Mathematics
Languages : en
Pages : 251
Get Book Here
Book Description
. . . 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.
Author: A. N. Parshin
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
Volume 62 of the Encyclopedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Written for the nonspecialist, the author assumes a general understanding of modern algebra and elementary number theory. Only the general properties of algebraic number fields and relate.
Author: Gerald J. Janusz
Publisher: American Mathematical Soc.
ISBN: 0821804294
Category : Mathematics
Languages : en
Pages : 288
Get Book Here
Book Description
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.
Author: Richard Dedekind
Publisher: Cambridge University Press
ISBN: 0521565189
Category : Mathematics
Languages : en
Pages : 170
Get Book Here
Book Description
A translation of a classic work by one of the truly great figures of mathematics.
Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
ISBN: 9780521004237
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
Book Description
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author: Edwin Weiss
Publisher: Courier Corporation
ISBN: 048615436X
Category : Mathematics
Languages : en
Pages : 308
Get Book Here
Book Description
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.
Author: M. Ram Murty
Publisher: Springer Science & Business Media
ISBN: 0387269983
Category : Mathematics
Languages : en
Pages : 354
Get Book Here
Book Description
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
