Apostol - Introduction to Analytic Number Theory (1976).pdf - Teoria liczb - Fermat

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

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

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 mathematicians are discussed

together with some of the techniques for sc!ving them.

One of the goals of this course has been to nurture the intrinsic interest

that many young mathematics students seem to have in number theory and

to open some doors for them to the current periodical literature. It has been

gratifying to note that many of the students who have taken this course

during the past 25 years have become professional mathematicians, and some

have made notable contributions of their own to number theory. To all of

them this book is dedicated.

’ The second volume is scheduled to appear in the Springer-Verlag Series Graduate Texts in

Mathematics under the title Modular Functions and Dirichlet Series in Number Theory.

Apostol - Introduction to Analytic Number Theory (1976).pdf

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