  Recently a function was constructed that satisfies all known properties of a
tree-level scattering of four massless scalars via the exchange of an infinite
tower of particles with masses given by the non-trivial zeroes of the Riemann
zeta function. A key ingredient in the construction is an even entire function
whose only zeroes coincide with the non-trivial zeroes of the Riemann zeta
function. In this paper we show that exactly the same conclusions can be drawn
for an infinite class of even entire functions with only zeroes on the real
line. This shows that the previous result does not seem to be connected to
specific properties of the Riemann zeta function, but it applies more
generally. As an application, we show that exactly the same conclusions can be
drawn for L-functions other than the Riemann zeta function.
