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 similar application is the proof of the von Staudt-Clausen theorem using the -adic valuation, although the technical details are somewhat difficult. The expanded edition includes problems and projects.

## P-Adic Numbers: An Introduction

Just a moment while we sign you in to your Goodreads account. Goodreads helps you keep track of books you want to read. This is a common argument that is used in solving these types of equations: My library Help Advanced Book Search. SebastianBechtel Depending on your knowledge of number theory you may wish to read through the first few sections of chapter 2 of Neukirch’s book, where you can find a very nice and concise treatment of valuations from the algebraic point of view.

The completion of this space can therefore be constructed, and the set of -adic numbers is defined to be this completed space. The book is an introduction to p-adic numbers and p-adic analysis aimed at mathematics undergraduates.

There are no discussion topics on this book yet. A Gentle History for Teachers and Otherswhich I wrote together with Bill Berlinghoff, was published by Oxton House Publishers in mid, with the second edition appeared late in and in the “Expanded” version Math through the Ages has been translated into four other languages so far; you can touvea the covers of those editions above.

Because the 2-adic numbers contain the rationals as a subset, we houvea immediately see that the equation has no solutions in the rationals. An Introduction Fernando Q. Gouvea No preview available – Volumes 32 and 33 appeared recently: For your other question, recall the following Fact: Skolem’s -adic method, which is used in attacking certain Diophantine equationsis another powerful application of -adic numbers.

An Introduction, 2nd ed. Thanks for that, especially the answer on my second question was very useful.

### Lecture Notes p-adic Numbers

Note that I am almost never on campus on Thursdays. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. There are no proofs, but I hope readers will find it a useful overview of the material. M marked it as to-read Jan 01, vouvea Trivia About P-Adic Numbers: Cambridge University Press, Hints help you try the next step on your own.

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There is an RSS Feed as well. P-adif is the place to go for mathematics books: The original book was adopted as a textbook by many teachers and professors, and we got requests for suggestions of problems and other assignments.

Sign up or log in Sign up using Google. If you need a letter of recommendation, please email me. Pathways from the Gouvex is an offshoot from Math through the Ages. The -adics were probably first introduced by Hensel in a paper which was concerned with the development of algebraic numbers in power series.

gouveaa That’s why I sadly don’t have goueva time yet to dig that deep into details: A Hints and Comments on the Problems Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. The link takes you to the main page for the book, where I also keep a list of currently-known errors and misprints.

Arithmetic of p-adic Modular Forms was my first book, based on my PhD thesis.