Sun Kai Leung

Multiplicative recurrence of Beatty and Piatetski-Shapiro sequences

Recurrence is a central theme in ergodic Ramsey theory. In this talk, I will present a sufficient condition for a set of natural numbers to be multiplicatively recurrent. As a consequence, inhomogeneous Beatty sequences and Piatetski–Shapiro sequences with small exponents exhibit multiplicative recurrence. This involves estimating the mean of unimodular completely multiplicative functions along these sequences. If time permits, I will also discuss the distribution of values taken by such functions along inhomogeneous Beatty and Piatetski–Shapiro sequences.