Share

Algebraic Numbers and Algebraic Functions

2005 Mathematics
Download Algebraic Numbers and Algebraic Functions PDF Online Free

Author :
Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 754/5 ( reviews)

GET EBOOK


Book Synopsis Algebraic Numbers and Algebraic Functions by : Emil Artin

Download or read book Algebraic Numbers and Algebraic Functions written by Emil Artin. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Number Theory

2000 Mathematics
Download Number Theory PDF Online Free

Author :
Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 544/5 ( reviews)

GET EBOOK


Book Synopsis Number Theory by : Helmut Koch

Download or read book Number Theory written by Helmut Koch. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Numbers and Algebraic Functions

1991-09-01 Mathematics
Download Algebraic Numbers and Algebraic Functions PDF Online Free

Author :
Release : 1991-09-01
Genre : Mathematics
Kind : eBook
Book Rating : 906/5 ( reviews)

GET EBOOK


Book Synopsis Algebraic Numbers and Algebraic Functions by : P.M. Cohn

Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn. This book was released on 1991-09-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Invitation To Algebraic Numbers And Algebraic Functions

2020-05-18 Mathematics
Download An Invitation To Algebraic Numbers And Algebraic Functions PDF Online Free

Author :
Release : 2020-05-18
Genre : Mathematics
Kind : eBook
Book Rating : 66X/5 ( reviews)

GET EBOOK


Book Synopsis An Invitation To Algebraic Numbers And Algebraic Functions by : Franz Halter-Koch

Download or read book An Invitation To Algebraic Numbers And Algebraic Functions written by Franz Halter-Koch. This book was released on 2020-05-18. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Algebraic Numbers and Algebraic Functions

2018-01-18 Mathematics
Download Algebraic Numbers and Algebraic Functions PDF Online Free

Author :
Release : 2018-01-18
Genre : Mathematics
Kind : eBook
Book Rating : 480/5 ( reviews)

GET EBOOK


Book Synopsis Algebraic Numbers and Algebraic Functions by : P.M. Cohn

Download or read book Algebraic Numbers and Algebraic Functions written by P.M. Cohn. This book was released on 2018-01-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...