Disjointness of Moebius from Horocycle Flows

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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].”
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures (2017, background): “From the Kátai-Bourgain-SarnakZiegler criterion [23, 2] (see also [33, 5]) one can show that if the claim (6) holds for 2k − 1, then it holds for k; we omit the details.”
Algebraic trace functions over the primes (2012, background): “Jean Bourgain pointed out that Theorem 2 of [6] (along with the Note following it) can be used in conjonction with (3.”
The logarithmic Sarnak conjecture for ergodic weights (2017, methodology): “The Sarnak conjecture has been proved for a variety of systems, for example nilsystems [32], some horocycle flows [6] and more general zero entropy systems arising from homogeneous dynamics [56], certain distal systems, in particular, some extensions of a rotation by a torus [45], [49], [67], a larg”