  We study Riemann-type functional equations with respect to value-distribution
theory and derive implications for their solutions. In particular, for a fixed
complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we
prove a Riemann-von Mangoldt formula for the number of a-points of the
$\Delta$-factor of the functional equation of $\mathcal{L}$ and an analog of
Landau's formula over these points. From the last formula we derive that the
ordinates of these $a$-points are uniformly distributed modulo one. Lastly, we
show the existence of the mean-value of the values of $\mathcal{L}(s)$ taken at
these points.
