Family 153Dynamical systems and ergodic theoryNo LeanNot yet digested
Arithmetic classification and non-Pisot singularity for Bernoulli convolutions
Classifies singular and absolutely continuous unbiased Bernoulli convolutions for every by an infinite, one-sided approximation condition using explicit finite sets of algebraic units. It also proves singularity at reciprocals of every quartic Salem number in , giving examples beyond reciprocal Pisot parameters.
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Arithmetic classification and non-Pisot singularity for Bernoulli convolutions
Oct 3, 2026·paper.pdf
We give an arithmetic classification of singular and absolutely continuous unbiased Bernoulli convolutions for every parameter . The criterion is expressed through one-sided approximation by explicitly defined finite sets of algebraic units; it is an infinite approximation condition, not a finite membership algorithm. We also establish singular examples beyond reciprocals of Pisot numbers: singularity holds at the reciprocal of every quartic Salem number in and at the reciprocal of a specified non-Pisot root of an explicit degree-31 polynomial.