On statistical properties of the Lerch zeta-function. II (Q1873258)

The Lerch zeta-function with parameters \(0<\lambda,\alpha\leq 1\) is given for \(\Re s>1\) by the Dirichlet series \[ L(\lambda,\alpha,s)=\sum_{n=0}^\infty {\exp(2\pi i\lambda)\over (n+\alpha)^s} \] and by analytic continuation elsewhere except for at most one simple pole at \(s=1\). In the present paper the author proves a discrete limit theorem for the Lerch zeta-function \(L(1,\alpha,s)\) (Hurwitz zeta-function) in the space of meromorphic functions. This paper is a continuation of the author's work [Lith. Math. J. 41, 330-343 (2001; Zbl 1028.11053)].