Problems in Analytic Number Theory
This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they
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206
Readings in Mathematics s. Axler
Editorial Board F.W. Gehring K.A. Ribet
Graduate Texts in Mathematics Readings in Mathematics EbbinghausJHennesfHirzebruchIKoecherlMainzerlNeukirchIPrestelJRemmert: Numbers FultonJHarris: Representation Theory: A First Course Murty: Problems in Analytic Number Theory Remmert: Theory o/Complex Functions Walter: Ordinary Differential Equations
Undergraduate Texts in Mathematics Readings in Mathematics Anglin: Mathematics: A Concise History and Philosophy Anglin!Lambek: The Heritage o/Thales Bressoud: Second Year Calculus HairerlWanner: Analysis by Its History HänunerlinJHoffrnann: Numerical Mathematics Isaac: The Pleasures 0/ Probability LaubenbacherlPengelley: Mathematical Expeditions: Chronicles by the Explorers Samuel: Projective Geometry Stillweil: Numbers and Geometry Toth: Glimpses 0/Algebra and Geometry
M. Ram Murty
Problems in Analytic Number Theory
Springer
M. RamMurty Department of Mathematics Queen's University Kingston, Ontario K7L 3N6 Canada
Editorial Board S. ruder
F.W. Gehring Mathematics Department East Hall University of Michigan Ann Arbor, M148109 USA
Mathematics Department San Francisco State University San Francisco, CA 94132 USA
K.A. Ribet Mathematics Department University of California at Berke1ey Berkeley, CA 94720-3840 USA
Cover photo by Dr. C.J. Mozzochi.
Mathematics Subject Classification (2000): 11Mxx, IlNxx Library of Congress Cataloging-in-Publication Data Murty, Maruti Ram. Problems in analytic nurnber theory I M. Ram Murty. p. cm. - (Graduate texts in mathematics ; 206) Includes bibliographical references and index. ISBN 978-1-4757-3443-0
ISBN 978-1-4757-3441-6 (eBook)
DOlI0.I007/978-1-4757-3441-6
1. Number theory. QA241 .M87 2000 512'.73-dc21
I. Title.
Printed on acid-free paper.
11. Series. 00-061865
2001 Springer-Verlag New York, Inc.
© 2001 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc in 2001. Softcover reprint of the hardcover 1 st edition 2001
All rights reserved. This work may not be translated or copied in whole or in part without the written permission ofthe publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrievaI, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be laken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Jenny Wolkowicki; manufacturing supervised by Jerome Basma. Camera-ready copy provided by the author. 987 6 543 2 I SPIN 10780694
Like fire in a piece of flint, knowledge exists in the mind. Suggestion is the friction which brings it out. - Vivekananda
