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eigenvalues of matrices or operators

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Series analyzed in Lubotzky–Phillips–Sarnak "Ramanujan Graphs"

In the LPS paper "Ramanujan graphs" the adjacency matrix of $X^{p,q}$, for simplicity say that $p,q\equiv1\mod{4}$ and $\left(\frac{p}{q}\right)=1$ (so, nonbipartite) and $n=\lvert X^{p,q}\rvert$, is …
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