Almost Mathieu operators with completely resonant phases
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abstract
Let $alphain mathbb{R}\backslash mathbb{Q}$ and $\beta(alpha) = limsup _{n o infty}(ln q_{n+1})/ q_n e^{2\beta(alpha)}$. In this paper, we developed a method to treat simultaneous frequency and phase resonances and obtain that for $2 hetain alpha mathbb{Z}+mathbb{Z}$, $H_{lambda,alpha, heta}$ satisfies Anderson localization if $|lambda|>e^{3\beta(alpha)}$.
