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On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions (1407.0776v2)
Published 3 Jul 2014 in math.NT
Abstract: Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits.