An atlas for all plane curves

Abstract

This note deals with an application of Voronin’s universality theorem for the Riemann zeta-function $\zeta$ . In particular, we show that every plane smooth curve appears, up to a small error, in the curve generated by the values $\zeta (\sigma +it)$ for real t, where $\sigma \in (1/2,1)$ is fixed. In this sense, the values of the zeta-function on any such vertical line provide an atlas for plane curves.