Hausdorff Dimension of a Class of Weierstrass Functions

It was proved by Shen that the graph of the classical Weierstrass function ∑;=;λ;cos（2πb;x） has Hausdorff dimension 2 + log λ/log b, for every integer b ≥ 2 and every λ∈（1/b, 1） [Hausdorff dimension of the graph of the classical Weierstrass functions, Math. Z., 289（2018）, 223–266]. In this paper, we prove that the dimension formula holds for every integer b ≥ 3 and every λ∈（1/b, 1） if we replace the function cos by sin in the definition of Weierstrass function. A class of more general functions are also discussed.