A Primer of Analytic Number Theory: From Pythagoras to Riemann

ISBN-13: 9780521012539 / Angielski / Miękka / 2003 / 400 str.

Jeffrey Stopple

Opis

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.

Recenzje

'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

Spis treści

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.