The joint universality and the functional independence for Lerch zeta-functions

Abstract

The joint universality theorem for Lerch zeta-functions $L(\lambda_l,\alpha_l,s)$ ($1\leq l \leq n$) is proved, in the case when $\lambda_l$s are rational numbers and $\alpha_l$s are transcendental numbers. The case $n=1$ was known before ([12]); the rationality of $\lambda_l$s is used to establish the theorem for the "joint" case $n\geq 2$. As a corollary, the joint functional independence for those functions is shown.