The central limit theorem for values of the Estermann function

This seminar will go into some detail into a proof of the central limit theorem for the values of the Estermann function D(x) at rationals x ordered by denominators, which we worked out with Sandro Bettin (Genova) in 2018. Here D(x) is the values at s=1/2 of the analytic continuation of the series

D(x, s) = \sum_{n>0} d(n) e^{2\pi i n x} / n^s.

We'll try to focus on the methods from dynamical systems theory which could be useful for other problems of number theory.