39 citations · 111 across the 20 of their papers we have counts for
28 papers
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…
Multiple recurrence and convergence without commutativity
Nikos Frantzikinakis, Bernard Host
We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our results…
A short proof of a conjecture of Erdös proved by Moreira, Richter and Robertson
Bernard Host
We give a short proof of a sumset conjecture of Erdös, recently proved by Moreira, Richter and Robertson: every subset of the integers of positive density contains the sum of two i…
Asymptotic pairs in positive-entropy systems
François Blanchard, Bernard Host, Sylvie Ruette
We show that in a topological dynamical system of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs such that and $\lim_{…
Furstenberg systems of bounded multiplicative functions and applications
Nikos Frantzikinakis, Bernard Host
We prove a structural result for measure preserving systems naturally associated with any finite collection of multiplicative functions that take values on the complex unit disc. W…
The logarithmic Sarnak conjecture for ergodic weights
Nikos Frantzikinakis, Bernard Host
The Möbius disjointness conjecture of Sarnak states that the Möbius function does not correlate with any bounded sequence of complex numbers arising from a topological dynamical sy…