On invariant measures for B-free systems

By Joanna Kuaga-PrzymusMariusz Lema, Barak Weiss. 2014

48 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Dynamics on the graph of the torus parametrization (2015, methodology): “G W ) 1 the lift of Haar measure on X toˆ MG W -Q GMG := m Xˆ(id ;G W ) 1 the lift of Haar measure on X toˆ GMG W Remark 3.8. In some cases, as e.g. the square-free integers and the B-free systems [34], the measure Q MG is called Mirsky measure. Note also that in the trivial case where m H(W) = 0, t”
Sarnak’s Conjecture: What’s New (2017, background): “For the Erdös case see [112] and for general B-free systems, see Theorem I in [17] (for further generalizations of B-free systems listed before (see page 51) no analogous description of the set of all invariant measures is known).”
Ergodic properties of visible lattice points (2015, methodology): “develop our notation and methods while we go along. Section 3 extends the ﬁndings to k-free points of n-dimensional lattices, while Section 4 looks into the setting of B-free systems as introduced in [18, 25]. Finally, in Section 5, we analyse an example from the number ﬁeld generalisation of [14] i”