The joint universality for pairs of zeta functions in the Selberg class

Abstract

We establish a joint universality theorem for pairs of functions in the Selberg class under certain conditions. This theorem generalizes and unifies several previous results, which were shown individually. We also give further examples of pairs of jointly universal L-functions, and actually extend the known universality theorem for the symmetric power L-function \({L(s, \mathrm{sym}^m f)}\) associated to a holomorphic Hecke eigen cusp form f for \({\mathrm{SL}_{2} (\mathbb{Z})}\) with \({1 \le m \le 4}\).