Equidistribution and related ergodic methods in number theory

Abstract

The thesis surveys some interesting equidistribution problems and ergodic methods pertinent to number theory. In chapter 1, the Weyl criterion is introduced and we study the relationship between some equidistribution problems and Riemann hypothesis. In chapter 2, we explore the Linnik problem- a classical problem concerning the spacial distribution of integral representations of integers by quadratic forms. In chapter 3, we study the dynamics of unimodular lattices under the action of the diagonal torus. The chapter ends with some applications of these ergodic methods.