p-adic Numbers : An Introduction. 3rd ed. 2020

種類:

電子ブック

責任表示:

by Fernando Q. Gouvêa

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Gouvêa, Fernando Q.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783030472955 [3030472957]    

注記:

1 Apéritif -- 2 Foundations -- 3 The p-adic Numbers -- 4 Exploring ℚp -- 5 Elementary Analysis in ℚp -- 6 Vector Spaces and Field Extensions -- 7 Analysis in ℂp -- 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.
There are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related to a chosen prime number p. They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students; this book provides an entryway to the subject for students with an undergraduate mathematics education. Readers who want to have an idea of and appreciation for the subject will probably find what they need in this book. Readers on the way to becoming experts can begin here before moving on to more advanced texts. This third edition has been thoroughly revised to correct mistakes, make the exposition clearer, and call attention to significant aspects that are usually reserved for advanced books. The most

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