Absolute continuity of complex Bernoulli convolutions

Pablo Shmerkin, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

Original languageEnglish
Pages (from-to)435-453
Number of pages19
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - 1 Nov 2016

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Copyright © Cambridge Philosophical Society 2016.


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