Absolute continuity of Bernoulli convolutions for algebraic parameters

Varjú, Péter

doi:10.1090/jams/916

Absolute continuity of Bernoulli convolutions for algebraic parameters
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by Péter P. Varjú

J. Amer. Math. Soc. 32 (2019), 351-397

DOI: https://doi.org/10.1090/jams/916

Published electronically: January 22, 2019

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Abstract:

We prove that Bernoulli convolutions $\mu _\lambda$ are absolutely continuous provided the parameter $\lambda$ is an algebraic number sufficiently close to $1$ depending on the Mahler measure of $\lambda$.

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