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A PRIMER OF ANALYTIC NUMBER THEORY
This undergraduate introduction to analytic number theory develops analytic
skills in the course of a study of ancient questions on polygonal numbers,
perfect numbers, and amicable pairs. The question of how the primes are
distributed among all integers is central in analytic number theory. This dis-
tribution is determined by the Riemann zeta function, and Riemann’s work
shows how it is connected to the zeros of his function and the significance of
the Riemann Hypothesis.
Starting from a traditional calculus course and assuming plex anal-
ysis, the author develops the basic ideas of elementary number theory. The
text is supplemented by a series of exercises to further develop the concepts
and includes brief sketches of more advanced ideas, to present contemporary
research problems at a level suitable for undergraduates. In addition to proofs,
both rigorous and heuristic, the book includes extensive graphics and tables
to make analytic concepts as concrete as possible.
Jeffrey Stopple is Professor of Mathematics at the University of California,
Santa Barbara.
A PRIMER OF ANALYTIC
NUMBER THEORY
From Pythagoras to Riemann
JEFFREY STOPPLE
University of California, Santa Barbara
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge , United Kingdom
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521813099
© Jeffrey Stopple 2003
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2003
isbn-13- 978-0-511-07316-8 eBook (EBL)
isbn-10- 0-511-07316-X eBook (EBL)
isbn-13-