2023/04/13 by Becher, Verónica, Marchionna, Agustín, Tenenbaum, Gérald
#11N60 #FOS: Mathematics #Number Theory (math.NT) #Primary 11K16 #Secondary 11N56
paper · doi:10.48550/arxiv.2304.06850
Given an integer b\geqslant 2 and a set P of prime numbers, the set TP of Toeplitz numbers comprises all elements of [0,b[ whose digits (an)n\geqslant 1 in the base-b expansion satisfy an=apn for all p∈ P and n\geqslant 1. Using a completely additive arithmetical function, we construct a number in~TP that is simply Borel normal if, and only if, ∑p\not ∈ P 1/p=∞. We then provide an effective bound for the discrepancy.