  The calculation of the minimum of the effective potential using the zeta
function method is extremely advantagous, because the zeta function is regular
at $s=0$ and we gain immediately a finite result for the effective potential
without the necessity of subtratction of any pole or the addition of infinite
counter-terms. The purpose of this paper is to explicitly point out how the
cancellation of the divergences occurs and that the zeta function method
implicitly uses the same procedure used by Bollini-Giambiagi and
Salam-Strathdee in order to gain finite part of functions with a simple pole.
