Stratified Universality

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1 \begin{table}[htbp]
2 \centering
3 \caption{Named prime-power seed families in local Euler coordinates.}
4 \label{tab:block07-named-local}
5 \scriptsize
6 \begin{tabularx}{\textwidth}{@{}L{0.24\textwidth}L{0.23\textwidth}L{0.25\textwidth}Y@{}}
7 \toprule
8 Arithmetic function & Nonzero local Euler exponents & Prime-power seed & Local ghost\\
9 \midrule
10 Constant-one function $\mathbf 1$ & $\beta_{1}=1$ & $1,1,1,1,1,1,\ldots$ & $1,1,1,1,1,1,\ldots$\\
11 M\"obius $\mu$ & $\beta_{1}=-1$ & $1,-1,0,0,0,0,\ldots$ & $-1,-1,-1,-1,-1,-1,\ldots$\\
12 Liouville $\lambda$ & $\beta_{1}=-1$, $\beta_{2}=1$ & $1,-1,1,-1,1,-1,\ldots$ & $-1,1,-1,1,-1,1,\ldots$\\
13 Squarefree indicator $\mu^2$ & $\beta_{1}=1$, $\beta_{2}=-1$ & $1,1,0,0,0,0,\ldots$ & $1,-1,1,-1,1,-1,\ldots$\\
14 Three-fold divisor function $\tau_3$ & $\beta_{1}=3$ & $1,3,6,10,15,21,\ldots$ & $3,3,3,3,3,3,\ldots$\\
15 \bottomrule
16 \end{tabularx}
17 \end{table}

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