  For the almost Mathieu operator $ (H_{\lambda,\alpha,\theta}u)
(n)=u(n+1)+u(n-1)+ \lambda v(\theta+n\alpha)u(n)$, Avila and Jitomirskaya guess
that for every phase $ \theta \in \mathscr{R} \triangleq\{\theta\in
\mathbb{R}\;| \; 2\theta + \alpha \mathbb{Z} \in \mathbb{Z}\}$,
$H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $ |\lambda| >
e^{ 2 \beta}$. In the present paper, we show that for every phase $ \theta \in
\mathscr{R} $, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $
|\lambda| > e^{ 7 \beta}$.
