Elementary And Analytic Theory Of Algebraic Numbers
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Author |
: Wladyslaw Narkiewicz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 732 |
Release |
: 2004-06-24 |
ISBN-10 |
: 3540219021 |
ISBN-13 |
: 9783540219026 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Elementary and Analytic Theory of Algebraic Numbers by : Wladyslaw Narkiewicz
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 |
: Wladyslaw Narkiewicz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 712 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662070017 |
ISBN-13 |
: 3662070014 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Elementary and Analytic Theory of Algebraic Numbers by : Wladyslaw Narkiewicz
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 |
: Helmut Koch |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 390 |
Release |
: 2000 |
ISBN-10 |
: 0821820540 |
ISBN-13 |
: 9780821820544 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Number Theory by : Helmut Koch
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 |
: H. P. F. Swinnerton-Dyer |
Publisher |
: Cambridge University Press |
Total Pages |
: 164 |
Release |
: 2001-02-22 |
ISBN-10 |
: 0521004233 |
ISBN-13 |
: 9780521004237 |
Rating |
: 4/5 (33 Downloads) |
Synopsis A Brief Guide to Algebraic Number Theory by : H. P. F. Swinnerton-Dyer
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author |
: Serge Lang |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 356 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9781461208532 |
ISBN-13 |
: 146120853X |
Rating |
: 4/5 (32 Downloads) |
Synopsis Algebraic Number Theory by : Serge Lang
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 |
: P. T. Bateman |
Publisher |
: World Scientific |
Total Pages |
: 378 |
Release |
: 2004 |
ISBN-10 |
: 9812560807 |
ISBN-13 |
: 9789812560803 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Analytic Number Theory by : P. T. Bateman
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (?elementary?) and complex variable (?analytic?) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/
Author |
: Jeffrey Stopple |
Publisher |
: Cambridge University Press |
Total Pages |
: 404 |
Release |
: 2003-06-23 |
ISBN-10 |
: 0521012538 |
ISBN-13 |
: 9780521012539 |
Rating |
: 4/5 (38 Downloads) |
Synopsis A Primer of Analytic Number Theory by : Jeffrey Stopple
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Author |
: M. Ram Murty |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 354 |
Release |
: 2005-09-28 |
ISBN-10 |
: 9780387269986 |
ISBN-13 |
: 0387269983 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Problems in Algebraic Number Theory by : M. Ram Murty
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 |
: Franz Halter-Koch |
Publisher |
: CRC Press |
Total Pages |
: 595 |
Release |
: 2020-05-04 |
ISBN-10 |
: 9780429014673 |
ISBN-13 |
: 0429014678 |
Rating |
: 4/5 (73 Downloads) |
Synopsis An Invitation To Algebraic Numbers And Algebraic Functions by : Franz Halter-Koch
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
Author |
: Andre Weil |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 332 |
Release |
: 2013-12-14 |
ISBN-10 |
: 9783662059784 |
ISBN-13 |
: 3662059789 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Basic Number Theory. by : Andre Weil
Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.