The high-dimensional Weierstrass functions

Haojie Ren, Weixiao Shen

For a real analytic periodic function $\varphi :\mathbb{R}\to {\mathbb{R}}^d$, an integer $b\ge 2$ and $\lambda \in (1/b,1)$, we prove that the box dimension and the Hausdorff dimension of the grap…