Singular non-Pisot Bernoulli convolutions

Abstract

We identify a family of numbers for which the Bernoulli convolution is singular. Within this family we find two countable collections of Salem numbers in the interval $(1,2)$, and another Salem number and an algebraic integer that is neither Pisot nor Salem in $(1,2)$. It also contains a non-Pisot, non-Salem algebraic number bigger than 3. Hence, we provide the first new explicit examples of singular Bernoulli convolutions since the work of Erdős in 1939.

12 pages, 3 figures, Mistake in proof

References in corpus (2)

• Absolute continuity of self-similar measures, their projections and convolutions
• Absolute continuity of Bernoulli convolutions for algebraic parameters