4 papers
A criterion for weighted uniform distribution along functions from a Hardy field
Michael Reilly
A classical theorem of Boshernitzan states that if is a function which belongs to a Hardy field and which satisfies for some , then t…
Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory
Vitaly Bergelson, Michael Reilly, Florian K. Richter
For a wide range of functions , we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))…
A Composition Theorem for Binomially Weighted Averages
Andy Liu, Michael Reilly
We study binomially weighted summation methods given by \[ (x_n)_{n\in \mathbb{N}} \mapsto \left(\sum_{k=0}^n\binom{n}{k}r^k(1-r)^{n-k}x_k\right)_{n\in \mathbb{N}} \] for $r\in (0,…
Uniform Weighted Averages and a Conjecture of Bergelson, Moreira, and Richter
Michael Reilly
We confirm a conjecture posed by Bergelson, Moreira, and Richter (arXiv:1711.05729), and in particular show that for every probability measure preserving system $(X,\mathscr{B},μ,…