Joint universality for Lerch zeta-functions

For $0<\alpha ,\lambda \le 1$, the Lerch zeta-function is defined by $L(s;\alpha ,\lambda )$$:= \sum_{n=0}^\infty e^{2\pi i\lambda n} (n+\alpha)^{-s}$,where$\sigma>1$. In this paper, we prove joint universality for Lerch zeta-functions with distinct ${\lambda }_1,\dots ,{\lambda }_m$ and transcendental $\alpha$.