Arithmetic version of anderson localization for quasiperiodic Schr\"odinger operators with even cosine type potentials

We propose a new method to prove Anderson localization for quasiperiodic Schr"odinger operators and apply it to the quasiperiodic model considered by Sinai and Fr"ohlich-Spencer-Wittwer. More concretely, we prove Anderson localization for even $C^2$ cosine type quasiperiodic Schr"odinger operators with large coupling constants, Diophantine frequencies and Diophantine phases.