Prime numbers and the Riemann hypothesis
By: Barry Mazur, Harvard University, Cambridge, MA, USA, William Stein, University of Washington, Seattle, WA, USA
Contributors: Stein, William A., 1974- author
Publisher: Cambridge University Press
Published: 2016
Language: eng
Number of pages: 142
ISBN-13: 9781107101920; 9781107499430
Subjects: Riemann hypothesis; Prime Numbers
Notes: Includes bibliographical references (pages 129-139) and index.
Table of contents: title: The Riemann Hypothesis. Thoughts about numbers ; What are prime numbers? ; "Named" prime numbers ; Sieves ; Questions about primes ; Further questions about primes ; How many primes are there? ; Prime numbers viewed from a distance ; Pure and applied mathematics ; A probabilistic first guess ; What is a "good approximation" ; Square root error and random walks ; What is Riemann's Hypothesis ; The mystery moves to the error term ; Cesàro smoothing ; A view of Li(X) - [pi](X) ; The prime number theorem ; The staircase of primes ; Tinkering with the staircase of primes ; Computer music files and prime numbers ; The word "spectrum" ; Spectra and trigonometric sums ; The spectrum and the staircase of primes ; To our readers of Part I; title: Distributions. Slopes of graphs that have no slopes ; Distributions ; Fourier Transforms : second visit ; Fourier Transform of delta ; Trigonometric series ; A sneak preview of Part III; title: - The Riemann Spectrum of prime numbers. On losing no information ; From primes to the Riemann Spectrum ; How many [theta][subscript i]'s are there? ; Further questions about the Riemann Spectrum ; From the Riemann Spectrum to primes; title: Back to Riemann. Building [pi](X) from the Spectrum ; As Riemann envisioned it ; Companions to the zeta function.