On universality of the Lerch zeta-function

It is known that the Lerch zeta-function $L(\lambda,\alpha,s)$ with transcendental parameter $\alpha$ is universal in the Voronin sense; i.e., every analytic function can be approximated by shifts $L(\lambda,\alpha,s+i\tau)$ uniformly on compact subsets of some region. In this paper, the universality for some classes of composite functions $F(L(\lambda,\alpha,s))$ is obtained. In particular, general theorems imply the universality of the functions $\sin(L(\lambda,\alpha,s))$ and $\sinh(L(\lambda,\alpha,s))$.