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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Burger and Struppeck show that for a prime and a positive integer. Table of contents 1 Aperitif.
Riccardo Giannitrapani added it Oct 31, Unlimited random practice problems and answers with built-in Step-by-step solutions. 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.
Infinite Series and p -adic Analysis. Cambridge University Press, Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory.
Other editions – View all p-adic Numbers: In language mathematicians will find familiar, this means all the ideas are motivated, but it goes beyond that. Olivierco added it Feb 10, Skolem’s -adic method, which is used in attacking certain Diophantine equationsis another powerful application of -adic numbers.
Unfortunately, in general, the answer is no, but there are classes of equations for which the answer is yes.
Nitin CR added it Dec 31, Trivia About P-Adic Numbers: This is a common argument that is used in solving these types of equations: More recently, p-adic num bers have shown up in other areas of mathematics, and even in physics. So we have an immediate proof of the irrationality of. Review quote From the reviews: Joao Alberto de Faria rated it really liked it Aug 08, Open Preview See a Problem?
Check out the top books of the year on our page Best Books of Account Options Sign in. Refresh and try again. An Introduction by Fernando Q. Return to Book Page. Looking for beautiful books? Chris Sharpe marked it as to-read Dec 06, Planck Constant added it Jun 19, Gouvea No preview available – If andthen the expansion is unique. Metal-Metal Bonding Gerard Parkin.
p-adic Number — from Wolfram MathWorld
Other books in this series. Wilhelmus Hendricus SchikhofC. P-Adic Numbers Fernando Q. Also define the -adic norm. Every rational has an “essentially” unique -adic expansion “essentially” since zero terms can always be added at the beginning. Jared marked it as to-read Mar 09, I find such problems very very difficult to get motivated by. The -adics were probably first introduced by Hensel in a paper which was concerned with the development of algebraic numbers in power series. Walk through homework problems step-by-step from beginning to end.
In the course of their undergraduate careers, most mathematics majors see little beyond “standard mathematics: P-Adic Numbers Fernando Q. 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.
P-Adic Numbers: An Introduction
Elementary Analysis in Qp I just learn better this way, there’s no doubt about it. Not only giving the background necessary to pursue the matter, but doing it in such a way that gouvwa healthy ‘hands-on experience’is generated in the process. Asking me to check you weren’t lying to me, when I know you aren’t lying or they would have caught it at the copyediting stage, is not going to get me excited. This elementary introduction offers a broad understanding of p-adic numbers.
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