The mgf of Pillai'sV(s)criterion in the central case has been obtained as a weighted sum of determinants whose elements are incomplete gamma functions. A method is given to reduce the determinants in terms of single integrals or their products. Exact upper 5 and 1 percent points are given forV(3)andV(4)(for selected values of an argumentn) using the expressions of the cdf obtained by inversion from the mgf for values of another argumentm= 1, 2, 3 fors=3, andm= 0, 1 fors= 4.