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Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 49,5 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author : J. S. Chahal
Publisher : Unknown
Page : 150 pages
File Size : 48,7 Mb
Release : 2003
Category : Algebraic number theory
ISBN : CORNELL:31924104903194
Author : M. Pohst,H. Zassenhaus
Publisher : Cambridge University Press
Page : 520 pages
File Size : 44,5 Mb
Release : 1997-09-25
Category : Mathematics
ISBN : 0521596696
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.
Author : Miles Reid,Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 312 pages
File Size : 42,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0521545188
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
Author : Richard A. Mollin
Publisher : CRC Press
Page : 424 pages
File Size : 51,9 Mb
Release : 2011-01-05
Category : Computers
ISBN : 9781439845998
Bringing the material up to date to reflect modern applications, this second edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. It offers a more complete and involved treatment of Galois theory, a more comprehensive section on Pollard's cubic factoring algorithm, and more detailed explanations of proofs to provide a sound understanding of challenging material. This edition also studies binary quadratic forms and compares the ideal and form class groups. The text includes convenient cross-referencing, a comprehensive index, and numerous exercises and applications.
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 676 pages
File Size : 49,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387216904
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 : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 43,8 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081
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
Author : Zhang Xian Ke
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
Page : 416 pages
File Size : 51,5 Mb
Release : 2016-03-14
Category : Mathematics
ISBN : 9781783323098
ALGEBRAIC NUMBER THEORY provides concisely both the fundamental and profound theory, starting from the succinct ideal theory (Chapters 1-3), turning then to valuation theory and local completion field (Chapters 4-5) which is the base of modern approach. After specific discussions on class numbers, units, quadratic and cyclotomic fields, and analytical theory (Chapters 6-8), the important Class Field Theory (Chapter 9) is expounded, and algebraic function field (Chapter 10) is sketched. This book is based on the study and lectures of the author at several universities.
Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459
A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.
Author : Henry Berthold Mann
Publisher : Unknown
Page : 190 pages
File Size : 49,7 Mb
Release : 1955
Category : Algebraic number theory
ISBN : UCAL:$B543539
Author : Edwin Weiss
Publisher : Courier Corporation
Page : 308 pages
File Size : 52,5 Mb
Release : 2012-01-27
Category : Mathematics
ISBN : 9780486154367
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 : Underwood Dudley
Publisher : MAA
Page : 156 pages
File Size : 43,7 Mb
Release : 2009
Category : Mathematics
ISBN : 0883853477
An introductory guide to elementary number theory for advanced undergraduates and graduates.
Author : Helmut Koch
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 51,9 Mb
Release : 2000
Category : Mathematics
ISBN : 0821820540
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 : Robert L. Long
Publisher : Unknown
Page : 216 pages
File Size : 46,6 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:39015015612396
Author : Richard Friedberg
Publisher : Courier Corporation
Page : 241 pages
File Size : 52,6 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486152691
This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.