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- W3005536004 abstract "Abstract We define a class of dynamical systems by modifying a construction due to Tao, which includes certain Furstenburg limits arising from the Liouville function. Most recent progress on the Chowla conjectures and sign patterns of the Mobius and Liouville functions uses methods that apply to any dynamical system in this class. Hence dynamical systems in this class with anomalous local behavior present obstructions to further progress on these problems by the same techniques. We construct straightforward examples of dynamical systems in this class based on polynomial phases and calculate the resulting obstruction. This requires explicit bounds for the number of sign patterns arising in a certain way from polynomials, which is elementary but not completely trivial." @default.
- W3005536004 created "2020-02-24" @default.
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- W3005536004 date "2020-08-01" @default.
- W3005536004 modified "2023-10-17" @default.
- W3005536004 title "Dynamical models for Liouville and obstructions to further progress on sign patterns" @default.
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- W3005536004 doi "https://doi.org/10.1016/j.jnt.2020.01.012" @default.
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