  We investigate the effect of long-range Coulomb interaction on the
quasiparticle properties and the dielectric function of clean three-dimensional
Weyl semimetals at zero temperature using a functional renormalization group
(FRG) approach. The Coulomb interaction is represented via a bosonic
Hubbard-Stratonovich field which couples to the fermionic density. We derive
truncated FRG flow equations for the fermionic and bosonic self-energies and
for the three-legged vertices with two fermionic and one bosonic external legs.
We consider two different cutoff schemes --- cutoff in fermionic or bosonic
propagators --- in order to calculate the renormalized quasiparticle velocity
and the dielectric function for an arbitrary number of Weyl nodes and the
interaction strength. If we approximate the dielectric function by its static
limit, our results for the velocity and the dielectric function are in good
agreement with that of A. A. Abrikosov and S. D. Beneslavski{\u{i}} [Sov. Phys.
JETP \textbf{32}, 699 (1971)] exhibiting slowly varying logarithmic momentum
dependence for small momenta. We extend their result for an arbitrary number of
Weyl nodes and finite frequency by evaluating the renormalized velocity in the
presence of dynamic screening and calculate the wave function renormalization.
