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Consider the one-dimensional lattice Schrödinger operator with potential given by the Moebius function. It is shown that the Lyapounov exponent is strictly positive for almost all energies, answering a question posed by P. Sarnak.
KeywordsMoebius Function Lyapounov Exponents Pointwise Closure Fubini Argument Banach Limit
The author is grateful to P. Sarnak for bringing the problem to his attention and several discussions. He also thanks H. Krüger for comments on how Theorem 1 in this note may be derived directly from Lemma 2 and the results in . The author was partially supported by NSF Grants DMS-0808042 and DMS 0835373.
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