to the p-adic number system as far as its metric and properties are concerned. . cation “p-adic Numbers: An Introduction”, by Fernando Q. Gouvêa. Proposition. () The p-adic numbers were first p n for a, b, n ∈ Z, where the prime p divides neither a nor b. p-adic norm . Fernando Q. Gouvea. p-adic Numbers, An . 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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A Hints and Comments on the Problems Both sets are available from Oxton House. Gouvea No preview available – A similar application is the proof of the von Staudt-Clausen theorem using the -adic valuation, although the technical details are somewhat difficult. Vector Spaces and Field Extensions.

The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. An Introduction Fernando Q. Patrick Whittle added it Feb 25, Suppose we have an equation that does have solutions in and in all the for every prime.

Lists with This Book. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The -adic numbers are useful in solving Diophantine equations.


Lecture Notes on p-adic Numbers

In the course of their undergraduate careers, most mathematics majors see little beyond “standard mathematics: So we have an immediate proof of the irrationality of.

My library Help Advanced Book Search. I’m working with Gouvea’s book on p-adic numbers.

Gouvea No preview available – History of Mathematics, especially the history of algebra and number theory, and Number Theory and Arithmetic Geometry, with a special focus on modular forms and Galois representations.

Olivierco added it Feb 10, Unfortunately I have very few knowledge in number theory. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. 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.

These corrections will go into the second printing of the second edition eventually. If I agree to write a letter, I may ask you for more information; the more you can provide, the better.

P-Adic Numbers: An Introduction

Practice online or make a printable study sheet. Edgar De marked it as to-read Nov 04, Any nonzero rational number can be represented by.

Check here for a few errata, notes, and other comments about the book. Email Required, but never shown. Joseph Stahl rated it p-adoc was amazing Jul 07, Joao Alberto de Faria rated it really liked it Aug 08, Then define the p -adic norm of by. If andthen the expansion is unique.


Fernando Q. Gouvêa’s Home Page

There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. Account Options Sign in. Want to Read saving…. Home Questions Tags P-adci Unanswered. Selected pages Title Page.

P-adic numbers : an introduction / Fernando Q. Gouvêa ; with 15 figures – Details – Trove

Thiago Dourado marked it as to-read Dec 15, Other editions – View all p-adic Numbers: For sufficiently large. Chris Aldrich added it Aug 03, There are no discussion topics on this book yet.

Peng Gao rated it liked it Dec 14, It can be shown that the rationals, together with the -adic gougea, do not form a complete metric space.