Gouvea p-adic Numbers

An Introduction
Erscheinungsjahr 2013
ISBN: 978-3-662-22278-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 282 Seiten, Web PDF

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Gouvea, Fernando Q.

Inhaltsverzeichnis

1 Apéritif.- 2 Foundations.- 3 p-adic Numbers.- 4 Elementary Analysis in ?
p.- 5 Vector Spaces and Field Extensions.- 6 Analysis in ?
p.- A Hints and Comments on the Problems.- B A Brief Glance at the Literature.- B.1 Texts.- B.2 Software.- B.3 Other books.