  We construct closed string vertex operators with various ghost numbers in
addition to the conventional ones, using the Faddeev-Popov procedure for the
gauge fixing of the conformal Killing group, from matter primary fields. We
find that these operators give solutions to the descent equations in the
framework of the BRST formalism. Similarly, we also construct solutions to the
descent equations for the dilaton vertex operator with the Lorentz covariant
form. Using the unintegrated vertex operator of the dilaton with the ghost
number three, we obtain the correct result of the tadpole amplitude on the
disk, including a non-zero contribution from a BRST exact term which comes from
a conformal transformation.
