Does anyone Know about an introductory book showing the intersection between ergodic theory, group actions and number theory? I have been looking for but it has been impossible to me. Thanks.
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There's this book on ergodic theory with a view towards number theory.
Also there's an expository article on the application of ergodic theory in analytic number theory.
I like the survey article "Interactions Between Ergodic Theory, Lie Groups, and. Number Theory" by Marina Ratner. Look it up in Google.