4 papers · 1 filter
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))…
Furstenberg--Sárközy theorem and partition regularity of polynomial equations over finite fields
Ethan Ackelsberg, Vitaly Bergelson
We prove new combinatorial results about polynomial configurations in large subsets of finite fields. Bergelson--Leibman--McCutcheon (2005) showed that for any polynomial $P(x) \in…
A note on polynomial equidistribution and recurrence in finite characteristic
Ethan Ackelsberg, Vitaly Bergelson
This paper addresses the topic of equidistribution and recurrence for polynomial sequences over function fields. The main focus is to note and correct two small errors in [V. Berge…
Weighted uniform distribution of subpolynomial functions along primes and applications
Vitaly Bergelson, Grigori Kolesnik, Younghwan Son
Let be a subpolynomial function in a Hardy field. We establish necessary and sufficient conditions for the weighted uniform distribution of the sequences $(u(n))_{n\in\mathb…