Analysis in \( \mathbb {C}_p \)
This chapter tries to give the reader a taste of what analysis in Cp is like. Rather than attempt to be exhaustive, which would violate the goals of this book, we try to touch on a few remarkable points: the p-adic Weierstrass Preparation Theorem, the des
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Fernando Q. Gouvêa
p-adic Numbers An Introduction Third Edition
Universitext
Universitext
Series Editors Sheldon Axler San Francisco State University Carles Casacuberta Universitat de Barcelona John Greenlees University of Warwick, Coventry Angus MacIntyre Queen Mary University of London Kenneth Ribet University of California, Berkeley Claude Sabbah École Polytechnique, CNRS, Université Paris-Saclay, Palaiseau Endre Süli University of Oxford Wojbor A. Woyczyński, Case Western Reserve University
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Fernando Q. Gouvêa
p-adic Numbers An Introduction Third Edition
Fernando Q. Gouvêa Department of Mathematics and Statistics Colby College Waterville, ME, USA
ISSN 0172-5939 ISSN 2191-6675 (electronic) Universitext ISBN 978-3-030-47294-8 ISBN 978-3-030-47295-5 (eBook) https://doi.org/10.1007/978-3-030-47295-5 Mathematics Subject Classification (2010): 11S80, 11-01, 12J25, 13F30 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
Introduction . . . . . . . . . . . . . . .
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