## 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 $\lambda$.## References

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## Bibliographic Information

**Péter P. Varjú**- Affiliation: Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Email: pv270@dpmms.cam.ac.uk
- Received by editor(s): August 16, 2016
- Received by editor(s) in revised form: May 15, 2017, and June 27, 2018
- Published electronically: January 22, 2019
- Additional Notes: The author gratefully acknowledges the support of the Royal Society.
- © Copyright 2019 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**32**(2019), 351-397 - MSC (2010): Primary 28A80, 42A85
- DOI: https://doi.org/10.1090/jams/916
- MathSciNet review: 3904156