  We investigate a possible difference between the effective potential and
zero-point energy. We define the zero-point ambiguity (ZPA) as the difference
between these two definitions of vacuum energy. Using the zeta function
technique, in order to obtain renormalized quantities, we show that ZPA
vanishes, implying that both of the above definitions of vacuum energy coincide
for a large class of geometries and a very general potential. In addition, we
show explicitly that an extra term, obtained by E. Myers some years ago for the
ZPA, disappears when a scale parameter $\mu$ is consistently introduced in all
zeta functions in order to keep them dimensionless.
