The Möbius function and distal flows
By Jianya Liu, Peter Sarnak. 2013
97 citations recorded by the source corpus.
We prove that the M\"{o}bius function is linearly disjoint from an analytic skew product on the $2$-torus. These flows are distal and can be irregular in the sense that their ergodic averages need not exist for all points. The previous cases for which such disjointness has been proved are all regular. We also establish the linear disjointness of M\"{o}bius from various distal homogeneous flows.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b8d891e03117e3de1c240f3c300651a6e5ccf83d
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
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- J. Kułaga-Przymus
- Mariusz Lemanczyk
- Sébastien Ferenczi
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Citations in the corpus
- The logarithmic Sarnak conjecture for ergodic weights (2017, background): “The Sarnak conjecture has been proved for a variety of systems, for example nilsystems [34], some horocycle flows [9] and more general zero entropy systems arising from homogeneous dynamics [59], certain distal systems, in particular some extensions of a rotation by a torus [47, 51, 70], a large cla”
- Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures (2016, unknown): “CHOWLA AND SARNAK CONJECTURES 3 dynamical systems [1], [2], [3], [5], [6], [7], [8], [9], [12], [13], [14], [15], [17], [18], [25], [29], [33], [39], [40], [41], [42], [43], [48], [49], [52], [58]; for further variants of the Sarnak conjecture, see [10], [13], [37].”
- Sarnak’s Conjecture: What’s New (2017, background): “In [120], we find examples of Anzai skew products which are minimal not uniquely ergodic but are Möbius disjoint,(80) moreover it is proved that if φ is analytic with an additional condition on the decay (from below) of Fourier coefficients then Tφ is Möbius disjoint for each irrational α.”