12 papers
Product sets in sets of returns and positivity of symmetric ergodic averages
Vitaly Bergelson, Saúl RodrÃguez-MartÃn, Saúl Rodríguez-Martín
We study sets of (measurable) returns in countable groups , namely sets of the form arising from measure-preserving actions. Extending a result of B…
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))…
Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments
Vitaly Bergelson, Florian K. Richter
Van der Waerden's theorem, published in Nieuw. Arch. Wisk. 15 (1927), acted as a catalyst for major further developments in Ramsey theory. In this survey, we delve into the legacy…
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…
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
Vitaly Bergelson, Joel Moreira, Florian K. Richter
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectur…