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Singular non-Pisot Bernoulli convolutions

2017/08/18 by Karma Dajani, Dajani, Karma, Charlene Kalle +1
Computer Science · Mathematics · #11K16 #37A05 #37H99 #42A85 #60J10 #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1708.05544

openalex publication_date 2017/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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