Introduction to P-adic Numbers and Valuation Theory
Author : George Bachman
Publisher :
Page : 173 pages
File Size : 43,36 MB
Release : 1964
Category :
ISBN : 9780120702688
Author : George Bachman
Publisher :
Page : 173 pages
File Size : 43,36 MB
Release : 1964
Category :
ISBN : 9780120702688
Author : George Bachman
Publisher :
Page : 196 pages
File Size : 26,38 MB
Release : 1964
Category : Algebraic fields
ISBN :
Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 17,3 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662222787
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.
Author : Fernando Q. Gouvêa
Publisher : Springer Nature
Page : 366 pages
File Size : 10,97 MB
Release : 2020-06-19
Category : Mathematics
ISBN : 3030472957
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
Author : Kurt Mahler
Publisher : CUP Archive
Page : 114 pages
File Size : 36,5 MB
Release : 1973-03-29
Category : Mathematics
ISBN :
Author : George Bachman
Publisher :
Page : pages
File Size : 37,5 MB
Release : 1964
Category :
ISBN :
Author : M. Ram Murty
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 45,87 MB
Release : 2009-02-09
Category : Mathematics
ISBN : 0821847740
This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 46,7 MB
Release : 1999-05-21
Category : Mathematics
ISBN : 9780387985251
Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.
Author : Linda Ann Curtis
Publisher :
Page : 196 pages
File Size : 44,88 MB
Release : 1978
Category :
ISBN :
Author : Antonio J. Engler
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 25,1 MB
Release : 2005-12-28
Category : Mathematics
ISBN : 354030035X
Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.