A Primer of Analytic Number Theory: From Pythagoras to Riemann

by Jeffrey Stopple

Overview

This undergraduate-level introduction describes those mathematical properties of prime numbers that can be deduced with the tools of calculus. Jeffrey Stopple pays special attention to the rich history of the subject and ancient questions on polygonal numbers, perfect numbers and amicable pairs, as well as to the important open problems. The culmination of the book is a brief presentation of the Riemann zeta function, which determines the distribution of prime numbers, and of the significance of the Riemann Hypothesis.

Product Details

ISBN-13:	9780521813099
Publisher:	Cambridge University Press
Publication date:	06/23/2003
Pages:	398
Product dimensions:	6.10(w) x 9.21(h) x 1.18(d)

Table of Contents

1. Sums and differences; 2. Products and divisibility; 3. Order and magnitude; 4. Counterexamples; 5. Averages; 6. Prime number theorems; 7. Series; 8. The Basel problem; 9. Euler's product; 10. The Riemann zeta function; 11. Pell's equation; 12. Elliptic curves; 13. Symmetry; 14. Explicit formula.

Editorial Reviews

"The book is interesting and, for a mathematics text, lively.... Stopple has done a particularly nice job with illustrations and tables that support the discussions in the chapters."
Chris Christensen, School Science and Mathematics

"… this is a well-written book at the level of senior undergraduates."
SIAM Review


"The book constitutes an excellent undergraduate introduction to classical analytical number theory. The author develops the subject from the very beginning in an extremely good and readable style. Although a wide variety of topics are presented in the book, the author has successfully placed a rich historical background to each of the discussed themes, which makes the text very lively … the text contains a rich supplement of exercises, brief sketches of more advanced ideas and extensive graphical support. The book can be recommended as a very good first introductory reading for all those who are seriously interested in analytical number theory."
EMS Newsletter


"… a very readable account."
Mathematika


"The general style is user-friendly and interactive … a well presented and stimulating informal introduction to a wide range of topics …"
Proceedings of the Edinburgh Mathematical Society

From the Publisher