Algebraic Numbers and Algebraic Functions 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 Algebraic Numbers and Algebraic Functions PDF full book. Access full book title Algebraic Numbers and Algebraic Functions by Emil Artin. Download full books in PDF and EPUB format.
Author: Emil Artin Publisher: American Mathematical Soc. ISBN: 0821840754 Category : Mathematics Languages : en Pages : 366
Book Description
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Author: Emil Artin Publisher: American Mathematical Soc. ISBN: 0821840754 Category : Mathematics Languages : en Pages : 366
Book Description
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Author: Helmut Koch Publisher: American Mathematical Soc. ISBN: 9780821820544 Category : Mathematics Languages : en Pages : 390
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: P.M. Cohn Publisher: CRC Press ISBN: 9780412361906 Category : Mathematics Languages : en Pages : 208
Book Description
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
Author: Harry Pollard Publisher: American Mathematical Soc. ISBN: 1614440093 Category : Mathematics Languages : en Pages : 175
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: Franz Halter-Koch Publisher: CRC Press ISBN: 042901466X Category : Mathematics Languages : en Pages : 708
Book Description
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: Henning Stichtenoth Publisher: Springer Science & Business Media ISBN: 3540768785 Category : Mathematics Languages : en Pages : 360
Book Description
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Author: E. T. Hecke Publisher: Springer Science & Business Media ISBN: 1475740921 Category : Mathematics Languages : en Pages : 251
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: M. Ram Murty Publisher: Springer Science & Business Media ISBN: 0387269983 Category : Mathematics Languages : en Pages : 354
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
Author: Emil Artin
Author: Emil Artin
Author: Helmut Koch
Author: P.M. Cohn
Author: Harry Pollard
Author: Franz Halter-Koch
Author: Harvey Cohn
Author: Emil Artin
Author: Henning Stichtenoth
Author: E. T. Hecke
Author: M. Ram Murty