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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Absolute continuity of Bernoulli convolutions for algebraic parameters
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by Péter P. Varjú PDF
J. Amer. Math. Soc. 32 (2019), 351-397 Request permission

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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Additional 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