On the application of discrete ergodic method in analytic theory of diophantine equations

In the talk, we will represent the basic results concerning the application of discrete ergodic method (DEM) in analytic theory of diophantine equations. The scheme of the talk is as follows:


1) Introduction. The basics of DEM.

2) The main results provided by DEM (ergodic properties of diophantine approximations and the theorems concerning the uniform distributions of solutions).

3) Further development of researching based on DEM.