A Primer of Analytic Number Theory: From Pythagoras to Riemann - ISBN:0521012538

A Primer of Analytic Number Theory: From Pythagoras to Riemann

Date: 08 May 2011, 00:31

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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.
Review
"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
Table of Contents
Preface
Chapter 1. Sums and Differences
Chapter 2. Products and Divisibility
Chapter 3. Order of Magnitude
Chapter 4. Averages
Interlude 1. Calculus
Chapter 5. Primes
Interlude 2. Series
Chapter 6. Basel Problem
Chapter 7. Euler's Product
Interlude 3. Complex Numbers
Chapter 8. The Riemann Zeta Function
Chapter 9. Symmetry
Chapter 10. Explicit Formula
Interlude 4. Modular Arithmetic
Chapter 11. Pell's Equation
Chapter 12. Elliptic Curves
Chapter 13. Analytic Theory of Algebraic Numbers
Solutions
Bibliography
Index
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