An exact renormalization formula for the Maryland model

We discuss the difference Schrödinger equation $ψ_{k+1}+ψ_{k-1}+λ\cot(πωk+θ)ψ_k=Eψ_k$, $k\in\mathbb{Z}$, where $λ$, $ω$, $θ$ and $E$ are parameters. We obtain explicit renormalization formulas relating its solutions for large $|k|$ to solutions of the equation with new parameters $λ$, $ω$, $θ$ and $E$ for bounded $|k|$. These formulas are similar to the renormalization formulas from the theory of Gaussian exponential sums.

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