文档介绍：Undergraduate Texts in Mathematics
Edilors
F. W. Gehring
P. R. Halmos
Advisory Board
C. DePrima
I. Herstein
J. Kiefer
W. LeVeque
Tom M. Apostol
Introduction
to Analytic
Number Theory
Springer-Verlag
New York Heidelberg Berlin
1976
Tom M. Apostol
Professor of Mathematics
California Institute of Technology
Pasadena. California 91 I25
AMS Subject Classification (1976)
10-01, 1OAXX
Library of Congress Cataloging in Publication Data
Apostol, Tom M.
Introduction to analytic number theory.
(Undergraduate texts in mathematics)
” Evolved from a course (Mathematics 160) offered
at the California Institute of Technology during the
last 25 years.”
Bibliography: p. 329
Includes index.
1. Numbers, Theory of. 2. Arithmetic functions.
3. Numbers, Prime. I. Title.
QA24l .A6 512’.73 75-37697
All rights reserved.
No part of this book may be translated or reproduced in
any form without written permission from Springer-Verlag.
@ 1976 by Springer-Verlag New York Inc.
Printed in the United States of America
ISBN o-387-90163-9 Springer-Verlag New York
ISBN 3-540-90163-9 Springer-Verlag Berlin Heidelberg
iv
Preface
This is the first volume of a two-volume textbook’ which evolved from a
course (Mathematics 160) offered at the California Institute of Technology
during the last 25 years. It provides an introduction to analytic number
theory suitable for undergraduates with some background in advanced
calculus, but with no previous knowledge of number theory. Actually, a
great deal of the book requires no calculus at all and could profitably be
studied by sophisticated high school students.
Number theory is such a vast and rich field that a one-year course cannot
do justice to all its parts. The choice of topics included here is intended to
provide some variety and some depth. Problems which have fascinated
generations of professional and amateur mathematici