rh.toc

\contentsline {chapter}{Preface}{5}{chapter*.2}
\contentsline {part}{I\hspace {1em}The Riemann Hypothesis{}}{11}{part.1}
\contentsline {chapter}{\numberline {1}Thoughts about numbers}{12}{chapter.1}
\contentsline {chapter}{\numberline {2}What are prime numbers?}{15}{chapter.2}
\contentsline {chapter}{\numberline {3}``Named'' prime numbers}{20}{chapter.3}
\contentsline {chapter}{\numberline {4}Sieves}{22}{chapter.4}
\contentsline {chapter}{\numberline {5}Questions about primes}{25}{chapter.5}
\contentsline {chapter}{\numberline {6}Further questions about primes}{28}{chapter.6}
\contentsline {chapter}{\numberline {7}How many primes are there?}{32}{chapter.7}
\contentsline {chapter}{\numberline {8}Prime numbers viewed from a distance}{37}{chapter.8}
\contentsline {chapter}{\numberline {9}Pure and applied mathematics}{39}{chapter.9}
\contentsline {chapter}{\numberline {10}A probabilistic first guess }{41}{chapter.10}
\contentsline {chapter}{\numberline {11}What is a ``good approximation''?}{45}{chapter.11}
\contentsline {chapter}{\numberline {12}Square root error and random walks}{47}{chapter.12}
\contentsline {chapter}{\numberline {13}What is Riemann's Hypothesis?}{49}{chapter.13}
\contentsline {chapter}{\numberline {14}The mystery moves to the error term}{51}{chapter.14}
\contentsline {chapter}{\numberline {15}Ces\`aro smoothing}{52}{chapter.15}
\contentsline {chapter}{\numberline {16} A view of $|\Li (X) - \pi (X)|$}{54}{chapter.16}
\contentsline {chapter}{\numberline {17}The Prime Number Theorem}{56}{chapter.17}
\contentsline {chapter}{\numberline {18}The staircase of primes}{60}{chapter.18}
\contentsline {chapter}{\numberline {19}Tinkering with the staircase of primes}{62}{chapter.19}
\contentsline {chapter}{\numberline {20}Computer music files and prime numbers}{65}{chapter.20}
\contentsline {chapter}{\numberline {21}The word ``Spectrum"}{71}{chapter.21}
\contentsline {chapter}{\numberline {22}Spectra and trigonometric sums }{73}{chapter.22}
\contentsline {chapter}{\numberline {23}The spectrum and the staircase of primes}{75}{chapter.23}
\contentsline {chapter}{\numberline {24}To our readers of Part\nobreakspace {}\ref {part1}}{77}{chapter.24}
\contentsline {part}{II\hspace {1em}Distributions}{78}{part.2}
\contentsline {chapter}{\numberline {25}Slopes of graphs that have no slopes}{79}{chapter.25}
\contentsline {chapter}{\numberline {26}Distributions}{86}{chapter.26}
\contentsline {chapter}{\numberline {27}Fourier transforms: second visit}{92}{chapter.27}
\contentsline {chapter}{\numberline {28}Fourier transform of delta}{95}{chapter.28}
\contentsline {chapter}{\numberline {29}Trigonometric series}{97}{chapter.29}
\contentsline {chapter}{\numberline {30}A sneak preview of Part\nobreakspace {}III}{99}{chapter.30}
\contentsline {part}{III\hspace {1em}The Riemann Spectrum of the Prime Numbers}{105}{part.3}
\contentsline {chapter}{\numberline {31}On losing no information}{106}{chapter.31}
\contentsline {chapter}{\numberline {32}From primes to the Riemann spectrum}{109}{chapter.32}
\contentsline {chapter}{\numberline {33}How many $\theta _i$'s are there?}{114}{chapter.33}
\contentsline {chapter}{\numberline {34}Further questions about the Riemann spectrum}{117}{chapter.34}
\contentsline {chapter}{\numberline {35}From the Riemann spectrum to primes}{119}{chapter.35}
\contentsline {part}{IV\hspace {1em}Back to Riemann}{121}{part.4}
\contentsline {chapter}{\numberline {36}Building $\pi (X)$ from the spectrum}{122}{chapter.36}
\contentsline {chapter}{\numberline {37}As Riemann envisioned it}{128}{chapter.37}
\contentsline {chapter}{\numberline {38}Companions to the zeta function}{135}{chapter.38}
\contentsline {chapter}{Endnotes}{141}{figure.38.6}