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 \draw[fill=black!10,draw=black!40,line width=.35pt] (2.57692,0.70000) rectangle ++(3.32308,3.50000);
3 \draw[->] (0.50000,2.45000) -- (6.10000,2.45000);
4 \draw[->] (0.90000,0.70000) -- (0.90000,4.40000);
5 \draw[dashed] (2.57692,0.70000) -- (2.57692,4.20000);
6 \draw[fill=white,line width=1pt] (2.57692,2.45000) circle (0.09);
7 \node[] at (2.57692,2.05000) {$1/2$};
8 \node[font=\sffamily\footnotesize] at (4.28000,3.22000) {series converges};
9 \node[] at (3.20000,4.85000) {$N=2$: $\mathfrak Z_N^{\rm red}(s)$};
10 \node[] at (3.20000,0.00000) {single continued pole at $s=1/2$};
11 \draw[fill=black!10,draw=black!40,line width=.35pt] (8.23846,0.70000) rectangle ++(4.36154,3.50000);
12 \draw[->] (7.20000,2.45000) -- (12.80000,2.45000);
13 \draw[->] (7.60000,0.70000) -- (7.60000,4.40000);
14 \draw[dashed] (8.23846,0.70000) -- (8.23846,4.20000);
15 \draw[fill=white,line width=1pt] (8.23846,2.45000) circle (0.09);
16 \node[] at (8.23846,2.05000) {$1/4$};
17 \node[font=\sffamily\footnotesize] at (10.98000,3.22000) {series converges};
18 \node[] at (9.90000,4.85000) {$N=4$: $\mathfrak Z_N^{\rm red}(s)$};
19 \node[] at (9.90000,0.00000) {single continued pole at $s=1/4$};
20 \end{tikzpicture}

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