39 citations · 166 across the 41 of their papers we have counts for
51 papers
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 +…
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…
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…
Partition regularity of generalized Pythagorean pairs
Nikos Frantzikinakis, Oleksiy Klurman, Joel Moreira
We address partition regularity problems for homogeneous quadratic equations. A consequence of our main results is that, under natural conditions on the coefficients , for a…
Bohr recurrence and density of non-lacunary semigroups of
Nikos Frantzikinakis, Bernard Host, Bryna Kra
A subset of integers is a set of Bohr recurrence if every rotation on returns arbitrarily close to zero under some non-zero multiple of . We show that the set…