39 citations · 166 across the 41 of their papers we have counts for
9 papers · 1 filter
Furstenberg systems of pretentious and MRT multiplicative functions
Nikos Frantzikinakis, Mariusz Lemańczyk, Thierry de la Rue
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious…
Correlations of multiplicative functions along deterministic and independent sequences
Nikos Frantzikinakis
We study correlations of multiplicative functions taken along deterministic sequences and sequences that satisfy certain linear independence assumptions. The results obtained exten…
Good weights for the Erdős discrepancy problem
Nikos Frantzikinakis
The Erdős discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progres…
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…
Ergodicity of the Liouville system implies the Chowla conjecture
Nikos Frantzikinakis
The Chowla conjecture asserts that the values of the Liouville function form a normal sequence of plus and minus ones. Reinterpreted in the language of ergodic theory it asserts th…