Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[anchor=west] at (0.30000,4.40000) {$q=1$};
3 \draw[fill=black!8,draw=black!40,line width=.35pt] (1.50000,4.10000) rectangle ++(8.75415,0.62000);
4 \draw[fill=black!20,draw=black!40,line width=.35pt] (10.25415,4.10000) rectangle ++(0.97268,0.62000);
5 \draw[fill=black!32,draw=black!40,line width=.35pt] (11.22683,4.10000) rectangle ++(0.35017,0.62000);
6 \draw[fill=black!44,draw=black!40,line width=.35pt] (11.57700,4.10000) rectangle ++(0.17866,0.62000);
7 \draw[fill=black!56,draw=black!40,line width=.35pt] (11.75566,4.10000) rectangle ++(0.10808,0.62000);
8 \draw[fill=black!75,draw=black!40,line width=.35pt] (11.86373,4.10000) rectangle ++(0.43627,0.62000);
9 \node[] at (6.80000,3.78000) {$\sigma_{2,1}=\frac{1}{2}$; first zero share $0.810569$};
10 \node[anchor=west] at (0.30000,3.10000) {$q=2$};
11 \draw[fill=black!8,draw=black!40,line width=.35pt] (1.50000,2.80000) rectangle ++(10.64377,0.62000);
12 \draw[fill=black!20,draw=black!40,line width=.35pt] (12.14377,2.80000) rectangle ++(0.13140,0.62000);
13 \draw[fill=black!32,draw=black!40,line width=.35pt] (12.27517,2.80000) rectangle ++(0.01703,0.62000);
14 \draw[fill=black!44,draw=black!40,line width=.35pt] (12.29221,2.80000) rectangle ++(0.00443,0.62000);
15 \draw[fill=black!56,draw=black!40,line width=.35pt] (12.29664,2.80000) rectangle ++(0.00162,0.62000);
16 \draw[fill=black!75,draw=black!40,line width=.35pt] (12.29826,2.80000) rectangle ++(0.00174,0.62000);
17 \node[] at (6.80000,2.48000) {$\sigma_{2,2}=\frac{1}{6}$; first zero share $0.985534$};
18 \node[anchor=west] at (0.30000,1.80000) {$q=3$};
19 \draw[fill=black!8,draw=black!40,line width=.35pt] (1.50000,1.50000) rectangle ++(10.78439,0.62000);
20 \draw[fill=black!20,draw=black!40,line width=.35pt] (12.28439,1.50000) rectangle ++(0.01479,0.62000);
21 \draw[fill=black!32,draw=black!40,line width=.35pt] (12.29919,1.50000) rectangle ++(0.00069,0.62000);
22 \draw[fill=black!44,draw=black!40,line width=.35pt] (12.29988,1.50000) rectangle ++(0.00009,0.62000);
23 \draw[fill=black!56,draw=black!40,line width=.35pt] (12.29997,1.50000) rectangle ++(0.00002,0.62000);
24 \draw[fill=black!75,draw=black!40,line width=.35pt] (12.29999,1.50000) rectangle ++(0.00001,0.62000);
25 \node[] at (6.80000,1.18000) {$\sigma_{2,3}=\frac{1}{15}$; first zero share $0.998555$};
26 \node[] at (6.80000,-0.55000) {five finite contributions plus the remaining tail; higher moments emphasize the nearest zero};
27 \end{tikzpicture}

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