Arithmetic Spectral Transitions for the Maryland Model
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abstract
We give a precise description of spectra of the Maryland model $ (h_{lambda,alpha, heta}u)_n=u_{n+1}+u_{n-1}+ lambda an pi( heta+nalpha)u_n$ for all values of parameters. We introduce an arithmetically defined index $delta (alpha, heta)$ and show that for $alpha otinmathbb{Q},,$ $sigma_{sc}(h_{lambda,alpha, heta})=overline{{e:gamma_{lambda}(e)
