Reference request : Ergodic theory and Number theory I would like to work on relations between Ergodic theory (or Dynamical systems) and Number theory. I am looking for a good reference book or lecture notes, and also I'd like to get familiar with articles and problems in this area. I checked similar questions that have been asked here but they didn't satisfy me. More precisely I want to know the research problems.
Thanks in advance
Maisam

The book "Ergodic theory: with a view towards Number Theory" by Einsiedler & Ward is an excellent intro to some standard results in ergodic theory (e.g. the ergodic theorems, mixing) and provides many number-theoretic applications (e.g. Szemeredi's theorem, the Gauss map, flows on quotients of $\mathbb{H}^2$). It is a graduate-level book, and I recommend a fluency in measure theory before you attempt to tackle it (it does have an appendix covering this material, but I think more conventional texts such as Rudin or Stein & Shakarchi would be more appropriate).
