  For the almost Mathieu operator
$(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda
\cos2\pi(\theta+n\alpha)u_n$, Avila and Jitomirskaya guess that for a.e.
$\theta$, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $
|\lambda| > e^{ \beta} $, and they establish this for $ |\lambda| >
e^{\frac{16}{9} \beta}$. In the present paper, we extend their result to regime
$ |\lambda| > e^{\frac{3}{2} \beta}$.

Spectral Theory