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 Erd\H{o}s in 1939.