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Author : Richard Dedekind
Publisher : Cambridge University Press
Page : 170 pages
File Size : 44,6 Mb
Release : 1996-09-28
Category : Mathematics
ISBN : 9780521565189
A translation of a classic work by one of the truly great figures of mathematics.
Author : E. T. Hecke
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 53,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740929
. . . 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 : Harry Pollard,Harold G. Diamond
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 54,5 Mb
Release : 1975-12-31
Category : Algebraic number theory
ISBN : 9781614440093
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
Page : 676 pages
File Size : 46,5 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 : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 53,9 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 : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 41,7 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 : Mak Trifković
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 52,8 Mb
Release : 2013-09-14
Category : Mathematics
ISBN : 9781461477174
By focusing on quadratic numbers, this advanced undergraduate or master’s level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group. The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms. The treatment of quadratic forms is somewhat more advanced than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader hands-on computational experience with elements and ideals in quadratic number fields. The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders. Prerequisites include elementary number theory and a basic familiarity with ring theory.
Author : David Hilbert
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 47,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662035450
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.
Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
Page : 712 pages
File Size : 41,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662070017
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.
Author : Harry Pollard
Publisher : Unknown
Page : 168 pages
File Size : 54,5 Mb
Release : 1961
Category : Algebraic fields
ISBN : UCAL:B5008744
Author : M. Ram Murty,Jody (Indigo) Esmonde
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 42,9 Mb
Release : 2005-09-28
Category : Mathematics
ISBN : 9780387269986
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
Author : Władysław Narkiewicz
Publisher : Springer
Page : 443 pages
File Size : 51,9 Mb
Release : 2019-01-18
Category : Mathematics
ISBN : 9783030037543
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.
Author : W Narkiewicz
Publisher : World Scientific Publishing Company
Page : 384 pages
File Size : 50,8 Mb
Release : 1984-02-01
Category : Mathematics
ISBN : 9789813104099
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.
Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 40,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461208532
This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS
Author : Frazer Jarvis
Publisher : Springer
Page : 298 pages
File Size : 53,9 Mb
Release : 2014-06-23
Category : Mathematics
ISBN : 9783319075457
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.