diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/papers/zeta/presentation/presentation.tex | 112 | ||||
| -rw-r--r-- | buch/papers/zeta/presentation/zeta_color_plot-img0.png | bin | 0 -> 37362 bytes | |||
| -rw-r--r-- | buch/papers/zeta/presentation/zeta_color_plot.pgf | 402 |
3 files changed, 509 insertions, 5 deletions
diff --git a/buch/papers/zeta/presentation/presentation.tex b/buch/papers/zeta/presentation/presentation.tex index bb6d515..be3e12c 100644 --- a/buch/papers/zeta/presentation/presentation.tex +++ b/buch/papers/zeta/presentation/presentation.tex @@ -80,6 +80,7 @@ \newcommand*{\RD}{\textcolor{red}} \newcommand*{\BL}{\textcolor{blue}} \newcommand*{\GN}{\textcolor{dgreen}} +\newcommand*{\YE}{\textcolor{violet}} @@ -242,20 +243,121 @@ \end{itemize} \end{frame} \begin{frame} + \frametitle{Euler Produkt: Verbindung von Zeta und Primzahlen} + \begin{equation*} + \zeta(s) + = + \sum_{n=1}^\infty + \frac{1}{n^s} + = + \prod_{p \in P} + \frac{1}{1-p^{-s}} + \end{equation*} + \pause + Geometrische Reihe + \begin{equation*} + \prod_{p \in P} + \frac{1}{1-p^{-s}} + = + \prod_{p \in P} + \left( + 1 + + + \frac{1}{p^s} + + + \frac{1}{p^{2s}} + + + \frac{1}{p^{3s}} + + + \ldots + \right) + \end{equation*} + \pause + Erste Terme ausmultiplizieren + \begin{align*} + \left( + 1 + + + \RD{\frac{1}{2^s}} + + + \GN{\frac{1}{2^{2s}}} + + + \frac{1}{2^{3s}} + + + \ldots + \right) + \left( + 1 + + + \BL{\frac{1}{3^s}} + + + \frac{1}{3^{2s}} + + + \frac{1}{3^{3s}} + + + \ldots + \right) + \left( + 1 + + + \YE{\frac{1}{5^s}} + + + \frac{1}{5^{2s}} + + + \frac{1}{5^{3s}} + + + \ldots + \right) + \\ + = + 1 + + + \RD{\frac{1}{2^s}} + + + \BL{\frac{1}{3^s}} + + + \GN{\frac{1}{4^s}} + + + \YE{\frac{1}{5^s}} + + + \ldots + \end{align*} + \end{frame} + \begin{frame} \frametitle{Primzahlfunktion} \begin{center} \scalebox{0.5}{\input{../primzahlfunktion.pgf}} \end{center} \end{frame} - \begin{frame} - \frametitle{Zusammenhang Zeta und Primzahlen} - %TODO - \end{frame} - \section{Weitere Eigenschaften} + \section{Darstellungen} + \begin{frame} + \frametitle{Farbcodierung} + \begin{center} + \scalebox{0.6}{\input{zeta_color_plot.pgf}} + \end{center} + \end{frame} + \begin{frame} + \frametitle{Konstanter Realteil $\Re(s)=-1$ und $\Im(s)=0\ldots40$} + \begin{center} + \scalebox{0.6}{\input{../zeta_re_-1_plot.pgf}} + \end{center} + \end{frame} + \begin{frame} + \frametitle{Konstanter Realteil $\Re(s)=0$ und $\Im(s)=0\ldots40$} + \begin{center} + \scalebox{0.6}{\input{../zeta_re_0_plot.pgf}} + \end{center} + \end{frame} + \begin{frame} + \frametitle{Konstanter Realteil $\Re(s)=0.5$ und $\Im(s)=0\ldots40$} + \begin{center} + \scalebox{0.6}{\input{../zeta_re_0.5_plot.pgf}} + \end{center} + \end{frame} \end{document} diff --git a/buch/papers/zeta/presentation/zeta_color_plot-img0.png b/buch/papers/zeta/presentation/zeta_color_plot-img0.png Binary files differnew file mode 100644 index 0000000..b8c7298 --- /dev/null +++ b/buch/papers/zeta/presentation/zeta_color_plot-img0.png diff --git a/buch/papers/zeta/presentation/zeta_color_plot.pgf b/buch/papers/zeta/presentation/zeta_color_plot.pgf new file mode 100644 index 0000000..0fd7cb8 --- /dev/null +++ b/buch/papers/zeta/presentation/zeta_color_plot.pgf @@ -0,0 +1,402 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{<filename>.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% and, on pdftex +%% \usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +%% +%% or, on luatex and xetex +%% \usepackage{unicode-math} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{<path to file>}{<filename>.pgf} +%% +%% Matplotlib used the following preamble +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.588156in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{3.971844in}{0.528000in}}% +\pgfpathlineto{\pgfqpoint{3.971844in}{4.224000in}}% +\pgfpathlineto{\pgfqpoint{2.588156in}{4.224000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{2.588156in}{0.528000in}}{\pgfqpoint{1.383688in}{3.696000in}}% +\pgfusepath{clip}% +\pgfsys@transformshift{2.588156in}{0.528000in}% +\pgftext[left,bottom]{\includegraphics[interpolate=true,width=1.390000in,height=3.700000in]{zeta_color_plot-img0.png}}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% 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