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[] at (3.72500,4.22000) {$2$};
3 \node[] at (6.37500,4.22000) {$z$};
4 \node[] at (9.02500,4.22000) {$z^{2}$};
5 \node[anchor=east] at (2.15000,3.37500) {$z^{3} + 1$};
6 \draw[fill=black!18,draw=black!40,line width=.35pt] (2.40000,2.95000) rectangle ++(2.65000,0.85000);
7 \node[] at (3.72500,3.37500) {$2 z^{3} + 2$};
8 \draw[fill=black!0,draw=black!40,line width=.35pt] (5.05000,2.95000) rectangle ++(2.65000,0.85000);
9 \node[] at (6.37500,3.37500) {$z^{4} + z$};
10 \draw[fill=black!0,draw=black!40,line width=.35pt] (7.70000,2.95000) rectangle ++(2.65000,0.85000);
11 \node[] at (9.02500,3.37500) {$z^{5} + z^{2}$};
12 \node[anchor=east] at (2.15000,2.52500) {$2 z$};
13 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.40000,2.10000) rectangle ++(2.65000,0.85000);
14 \node[] at (3.72500,2.52500) {$4 z$};
15 \draw[fill=black!0,draw=black!40,line width=.35pt] (5.05000,2.10000) rectangle ++(2.65000,0.85000);
16 \node[] at (6.37500,2.52500) {$2 z^{2}$};
17 \draw[fill=black!18,draw=black!40,line width=.35pt] (7.70000,2.10000) rectangle ++(2.65000,0.85000);
18 \node[] at (9.02500,2.52500) {$2 z^{3}$};
19 \node[anchor=east] at (2.15000,1.67500) {$3 z^{2}$};
20 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.40000,1.25000) rectangle ++(2.65000,0.85000);
21 \node[] at (3.72500,1.67500) {$6 z^{2}$};
22 \draw[fill=black!18,draw=black!40,line width=.35pt] (5.05000,1.25000) rectangle ++(2.65000,0.85000);
23 \node[] at (6.37500,1.67500) {$3 z^{3}$};
24 \draw[fill=black!0,draw=black!40,line width=.35pt] (7.70000,1.25000) rectangle ++(2.65000,0.85000);
25 \node[] at (9.02500,1.67500) {$3 z^{4}$};
26 \node[] at (6.20000,0.25000) {$\mathcal B_{3,0}(FG)=2+7z^3$};
27 \node[] at (6.20000,-0.40000) {shaded cells: $(0,0), (1,2), (2,1)$ all land in residue $0$};
28 \end{tikzpicture}

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