Discrete universality of the L-functions of elliptic curves

Abstract

A discrete universality theorem is obtained in the Voronin sense for the L-functions of elliptic curves. We use the difference of an arithmetical progression h > 0 such that \( \exp \left\{ {\frac{{2\pi k}} {h}} \right\} \) is rational for some k ≠ 0. A limit theorem in the space of analytic functions plays a crucial role in the proof.