p-adic Numbers: An Introduction

Fernando Q. Gouvea - Collection Yellow Sale 2023

366 pages, parution le 19/06/2020

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Résumé

There are numbers of all kinds: rational, real, complex, p-adic. This elementary introduction offers a broad understanding of p-adic numbers.

From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is."

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers.

From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE

1 Aperitif.- 2 Foundations.- 3 The p -adic Numbers.- 4 Exploring _p .- 5 Elementary Analysis in _p .- 6 Vector Spaces and Field Extensions.- 7 Analysis in _p .- 8 Fun With Your New Head.- A Sage and GP: A (Very) Quick Introduction.- B Hints and Comments on the Problems.- C A Brief Glance at the Literature.- Bibliography.- Index.Fernando Q. Gouvea is a number theorist and historian of mathematics. In number theory he has been interested in the connection between p -adic modular forms and deformations of Galois representations. As a historian his main focus is on the early history of algebraic number theory, but he has also written on other historical topics. He enjoys books and has written many book reviews for a wide range of publications. For many years he served as editor of MAA Focus and of MAA Reviews. His current project is a forthcoming book on the history of p -adic numbers and p -adic analysis in the first decades of the twentieth century. Gouvea's other books include Arithmetic of p-adic Modular Forms , A Guide to Groups, Rings, and Fields , and (with William P. Berlinghoff) Math through the Ages: A Gentle History for Teachers and Others .