Number Theory Introduction To Class Field Theory PDF Download
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Author | : Nancy Childress |
Publisher | : Springer Science & Business Media |
Total Pages | : 230 |
Release | : 2008-10-28 |
Genre | : Mathematics |
ISBN | : 0387724907 |
Download Class Field Theory Book in PDF, ePub and Kindle
Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.
Author | : Kazuya Kato |
Publisher | : |
Total Pages | : |
Release | : 2000 |
Genre | : Number theory |
ISBN | : |
Download Number Theory: Introduction to class field theory Book in PDF, ePub and Kindle
Author | : Kazuya Kato |
Publisher | : American Mathematical Soc. |
Total Pages | : 180 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821808634 |
Download Number Theory 1 Book in PDF, ePub and Kindle
This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.
Author | : Pierre Guillot |
Publisher | : Cambridge University Press |
Total Pages | : 309 |
Release | : 2018-11 |
Genre | : Mathematics |
ISBN | : 1108421776 |
Download A Gentle Course in Local Class Field Theory Book in PDF, ePub and Kindle
A self-contained exposition of local class field theory for students in advanced algebra.
Author | : Harvey Cohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461299500 |
Download A Classical Invitation to Algebraic Numbers and Class Fields Book in PDF, ePub and Kindle
"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Author | : Helmut Koch |
Publisher | : American Mathematical Soc. |
Total Pages | : 390 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821820544 |
Download Number Theory Book in PDF, ePub and Kindle
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 | : Jürgen Neukirch |
Publisher | : Springer Science & Business Media |
Total Pages | : 195 |
Release | : 2013-04-08 |
Genre | : Mathematics |
ISBN | : 3642354378 |
Download Class Field Theory Book in PDF, ePub and Kindle
The present manuscript is an improved edition of a text that first appeared under the same title in Bonner Mathematische Schriften, no.26, and originated from a series of lectures given by the author in 1965/66 in Wolfgang Krull's seminar in Bonn. Its main goal is to provide the reader, acquainted with the basics of algebraic number theory, a quick and immediate access to class field theory. This script consists of three parts, the first of which discusses the cohomology of finite groups. The second part discusses local class field theory, and the third part concerns the class field theory of finite algebraic number fields.
Author | : Edwin Weiss |
Publisher | : Courier Corporation |
Total Pages | : 308 |
Release | : 2012-01-27 |
Genre | : Mathematics |
ISBN | : 048615436X |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
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 | : Daniel A. Marcus |
Publisher | : Springer |
Total Pages | : 203 |
Release | : 2018-07-05 |
Genre | : Mathematics |
ISBN | : 3319902334 |
Download Number Fields Book in PDF, ePub and Kindle
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Author | : Michael Rosen |
Publisher | : Springer Science & Business Media |
Total Pages | : 355 |
Release | : 2013-04-18 |
Genre | : Mathematics |
ISBN | : 1475760469 |
Download Number Theory in Function Fields Book in PDF, ePub and Kindle
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.