Computing Garsia entropy for Bernoulli convolutions with algebraic parameters * *Research of K G Hare was supported by NSERC Grant 2019-03930.

Abstract

We introduce a parameter space containing all algebraic integers β ∈ (1, 2] that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ν β . This allows us to show that dimH(ν β ) = 1 for all β with representations in certain open regions of the parameter space.