5 papers
Weighted averages and applications to sets of multiple recurrence
Vitaly Bergelson, Michael Reilly
We introduce new techniques for determining combinatorial properties of sets of multiple recurrence by considering weighted averages with quickly growing weights. Our main result i…
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,T…