9 papers
Seminorm control for ergodic averages with commuting transformations and pairwise dependent polynomial iterates
Nikos Frantzikinakis, Borys Kuca
We examine multiple ergodic averages of commuting transformations with polynomial iterates in which the polynomials may be pairwise dependent. In particular, we show that such aver…
Ergodic averages for sparse corners
Nikos Frantzikinakis, Borys Kuca
We develop a framework for the study of the limiting behavior of multiple ergodic averages with commuting transformations when all iterates are given by the same sparse sequence; t…
Recurrence for pretentious systems along generalized Pythagorean triples
Nikos Frantzikinakis, Andreas Mountakis
We establish multiple recurrence results for pretentious measure-preserving multiplicative actions along generalized Pythagorean triples, that is, solutions to the equation $ax^2 +…
Partition regularity of homogeneous quadratics: Current trends and challenges
Nikos Frantzikinakis
Suppose we partition the integers into finitely many cells. Can we always find a solution of the equation with on the same cell? What about more general homog…
Decomposition results for multiplicative actions and applications
Nikos Frantzikinakis
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions wi…
Joint ergodicity for commuting transformations and applications to polynomial sequences
Nikos Frantzikinakis, Borys Kuca
We give necessary and sufficient conditions for joint ergodicity results of collections of sequences with respect to systems of commuting measure preserving transformations. Combin…