文档介绍：ANALYTI
NUMBER
THEOR
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ANALYTIC
NUMBER
THEORY
An Introductory Course
Paul T Bateman
Harold G Diamond
University of Illinois at Urbana-Champaign
World Scientific
BEIJING . SHANGHAI . HONG KONG . TAIPEI . CHENNAI
Published by
World Scientific Publishing Co. Re. Ltd.
5 Toh Tuck Link, Singapore 596224
USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-PublicationData
A catalogue record for this book is available from the British Library.
ANALYTIC NUMBER THEORY - AN INTRODUCTORY COURSE
Copyright 0 2004 by World Scientific Publishing Co. Re. Ltd.
All rights reserved. This book, or parts thereoJ may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-238-938-5
981-256-080-7 (pbk)
This book is printed on acid-free paper.
Printed in Singapore by Mainland Press-
To OUT wives, Felice and Nancy
Preface
Number theory holds a distinguished position in mathematics for its many
results which are at once profound and yet easy to state. It is a beautiful
subject, and we hope this book will invite students to its study.
Our theme is the use of analysis to treat multiplicative problems in
number theory. We study several of the principal methods and results in
this area, particularly those involving reasonably stable arithmetical enti-
ties. Typical examples include counts of integers having regularly occurring
properties or summatory functions of arithmetic fun