Hausdorff Dimension of a Class of Weierstrass Functions

It was proved by Shen that the graph of the classical Weierstrass function Sigma(infinity)(n =0) lambda(n) cos(2 pi b(n)x) has Hausdorff dimension 2 + log lambda/log b, for every integer b >= 2 and every l is an element of(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 lambda is an element of(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.