  The probabilistic study of the value-distributions of zeta-functions is one
of the modern topics in analytic number theory. In this paper, we study a
certain probability measure related to the value-distribution of the Lerch
zeta-function. We prove that it has a density function which we can explicitly
construct. Moreover, we prove an asymptotic formula for the number of zeros of
the Lerch zeta-function on the right side of the critical line, whose main term
is associated with the density function.
