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Singular non-Pisot Bernoulli convolutions (1708.05544v2)
Published 18 Aug 2017 in math.DS
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.