A Dichotomy for the Weierstrass-type functions

Haojie Ren, Weixiao Shen

For a real analytic periodic function $\varphi :\mathbb{R}\to \mathbb{R}$, an integer $b\ge 2$ and $\lambda \in (1/b,1)$, we prove the following dichotomy for the Weierstrass-type function $W(x)…