Introduction to Analytic Number Theory, Volume 1

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Springer Science & Business Media, May 11, 1976 - Mathematics - 338 pages
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to Analytic Number Theory With 24 Illustrations ~Springer Tom M. Apostol Department of Mathematics California Institute ofTechnology Pasadena, California 91125 U.S.A. Editorial Board S. Axler F.W. Gehring K.A. Ribet Mathematics Department Mathematics Department Mathematics Department San Francisco State East Hali University of California, University University of Michigan at Berkeley San Francisco, CA 94132 Ann Arbor, MI 48109 Berkeley, CA 94720-3840 USA USA USA Mathematics Subject Classification (2000): 11-01, Il AXX Library of Congress Cataloging-in-Publication Data Apostol, Tom M. lntroduction to analytic number theory. (Undergraduate texts in mathematics) "Evolved from a course (Mathematics 160) offered at the California Institute ofTechnology during the last 25 years." Bibliography: p. 329. lncludes index. 1. Numbers, Theory of. 2. Arithmetic functions. 3. Numbers, Prime. !. Title. Printed on acid-frec paper. QA24l.A6 512 '73 75-3 7697 ISBN 978-1-4419-2805-4 ISBN 978-1-4757-5579-4 (eBook) DOI 10.1007/978-1-4757-5579-4 1976 Springer Science+Business Media New York Originally published by Springer Science+Business Media, Inc. in 1976 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scho1arly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimi1ar methodology now known or hereafter developed is forbidden.
  

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I've found this to be the best overall introduction to analytic number theory. I'm trained in physics, and interested in number theory, and this book really helped me to learn the basics. The problems are excellent as well.

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This is the best book I ever found in Analytic Number Theory. It had given history of number theory in brief, which is also inspiring. Chapter 1 deals with Fundamental Theorem of Arithmetic. In this chapter divisiblity, greatest common factor, prime numbers etc etc are explained in very nice manner.
The arrangement of chapters are very nice. It starts with easy topics and ending with more difficult chapters. I would like to say that this is topmost beautiful book in area of NUMBER THEORY.
 

Contents

Historical Introduction
1
The Fundamental Theorem of Arithmetic
13
Chapter
14
The Euclidean algorithm
19
Chapter 3
52
Chapter 4
71
Chapter 5
106
Chapter 6
129
Chapter 9
177
Primitive Roots
204
Chapter 11
223
Chapter 12
249
Chapter 13
278
Partitions
304
Bibliography
329
Index
335

Chapter 7
146
Periodic Arithmetical Functions and Gauss Sums
157

Common terms and phrases

References to this book

Permutation Groups
John D. Dixon
Limited preview - 1996
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About the author (1976)

Tom M. Apostol joined the California Institute of Technology faculty in 1950 and is now Professor of Mathematics, Emeritus. He is internationally known for his textbooks on Calculus, Analysis, and Analytic Number Theory, which have been translated into 5 languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. His list of publications includes 98 research papers, 46 of them published since he retired in 1992. He has received several awards for his research and teaching. In 1978 he was a visiting professor at the University of Patras in Greece, and in 2000 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek.

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