Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On arithmetic functions orthogonal to deterministic sequences   We prove Veech's conjecture on the equivalence of Sarnak's conjecture on
M\"obius orthogonality with a Kolmogorov type property of Furstenberg systems
of the M\''obius function. This yields a combinatorial condition on the
M\"obius function itself which is equivalent to Sarnak's conjecture. As a
matter of fact, our arguments remain valid in a larger context: we characterize
all bounded arithmetic functions orthogonal to all topological systems whose
all ergodic measures yield systems from a fixed characteristic class (zero
entropy class is an example of such a characteristic class) with the
characterization persisting in the logarithmic setup. As a corollary, we obtain
that the logarithmic Sarnak's conjecture holds if and only if the logarithmic
M\''obius orthogonality is satisfied for all dynamical systems whose ergodic
measures yield nilsystems.

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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph