ON THE DEFICIENCIES OF COMPOSITE ENTIRE-FUNCTIONS

For any sequence (a(j)) of complex numbers and for any rho > 1/2- we construct an entire function F with the following properties. F has order rho, mean type, each a(j) is a deficient value of F, and F is given by F(z)=f(g(z)), where f and g are transcendental entire functions. This complements a result of Goldstein. We also construct, for any rho > 1/2, an entire function G of order rho, mean type, such that lim inf(r --> infinity) T(r,G)/T(rG')>1.