The p-adic norm and the p-adic numbers. Chapter 3. Some elementary p-adic analysis. Chapter 4. The topology of Qp. Chapter 5. p-adic algebraic. P-Adic Numbers has 8 ratings and 1 review. Ben said: I really love the way Gouvea writes about math. There are two things I love in particular:1) He is. To my eyes, the most glaring omission was a book by Fernando Gouvêa, originally published in , entitled p-adic Numbers: An Introduction.
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Daniel rated it really liked it Dec 25, Olivierco added it Feb 10, Can we conclude that the equation has a solution in? Also define the -adic norm. The overall conclusion is simple: Erik De Laet marked it as to-read May 09, Algebraic Numbers and Functions.
Peng Gao rated it liked it Dec 14, Paperbackpages. For sufficiently large. There are numbers of goivea kinds: The completion of this space can therefore be constructed, and the set of -adic numbers is defined to be this completed space.
p-adic Numbers : An Introduction
Thanks for telling us about the problem. Robbie added it Jan 25, Unfortunately, in general, the answer is no, but there are classes of equations for which the answer is yes. Home Contact Us Help Free delivery worldwide.
In the course of their undergraduate careers, most mathematics majors see little beyond “standard mathematics: There are no discussion topics on this book yet.
The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Adjoining a p-th Root of Unity. Walk through homework problems step-by-step from beginning to end.
B A Brief Glance at the Literature. Gouvea No preview available – Seventh International Conference on P-Adic Gouvea has succeeded admirably in taking a topic that is not standard in the undergraduate mathematics curriculum and writing a book accessible to undergraduates that allows its reader to play with some aeic mathematics and explore a topic which is both fun and important.
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p-adic Numbers: An Introduction – Fernando Gouvea – Google Books
Wilhelmus Hendricus SchikhofC. This is a common argument that is used in solving these types of equations: Another application is the theorem that the harmonic numbers are never integers except for. A New Kind of Science. Cambridge University Press, Table of contents 1 Aperitif.
P-adic Numbers and Their Functions, 2nd ed. Practice online or make a printable study sheet. Goodreads helps you keep track of books you want to read. Avana marked it as to-read Jun 07, Want to Read saving….
There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. This equation has no solutions in because it has no solutions in the realsand is a subset of. An Introduction by Fernando Q. Shyan rated it it was amazing May 26, There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics.
Add Staples marked it as to-read Aug 09, Books by Fernando Q.
Sundar Iyer rated it really liked it Jan 11, In language mathematicians will find familiar, this means all the ideas are motivated, but it goes beyond that. To ask other readers questions about P-Adic Numbersplease sign up. Just as the real numbers are the completion of the rationals with respect to the usual absolute valuationthe -adic numbers are the completion of with respect to the -adic valuation. The -adic numbers are useful in solving Diophantine equations.
Now consider the converse. A -adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime are related to proximity in the so called ” -adic metric.
This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems.