The Prime Numbers and Their Distribution
About this Title
Gérald Tenenbaum, Université Henri Poincaré, Nancy I, France and Michel Mendès France, Université Bordeaux I, Bordeaux, France. Translated by Philip G. Spain
Publication: The Student Mathematical Library
Publication Year 2000: Volume 6
ISBNs: 978-0-8218-1647-9 (print); 978-1-4704-2125-0 (online)
MathSciNet review: MR1756233
MSC: Primary 11N05; Secondary 11A41, 11N13
One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness.
The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem.
This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
Advanced undergraduates, graduate students, and research mathematicians.
Table of Contents
- Chapter 1. Genesis: From Euclid to Chebyshev
- Chapter 2. The Riemann zeta function
- Chapter 3. Stochastic distribution of prime numbers
- Chapter 4. An elementary proof of the prime number theorem
- Chapter 5. The major conjectures