  For $0 < a \le 1/2$, we define the quadrilateral zeta function $Q(s,a)$ using
the Hurwitz and periodic zeta functions and show that $Q(s,a)$ satisfies
Riemann's functional equation studied by Hamburger, Heck and Knopp. Moreover,
we prove that for any $0 < a \le 1/2$, there exist positive constants $A(a)$
and $T_0(a)$ such that the number of zeros of the quadrilateral zeta function
$Q(s,a)$ on the line segment from $1/2$ to $1/2 +iT$ is greater than $A(a) T$
whenever $T \ge T_0(a)$.
