Fractal curves from prime trigonometric series

Dimitris Vartziotis, Doris Bohnet

We study the convergence of the parameter family of series $$V_{\alpha ,\beta }(t)=\sum _p{p}^{-\alpha }\exp (2\pi i{p}^{\beta }t),\alpha ,\beta \in {\mathbb{R}}_{>0},t\in [0,1)$$ defined over prime numbers $p$, a…