121 Lasse Asikainen

Lasse Asikainen (University of Eastern Finland)// A new proximity function estimate on the quotient of the difference and the derivative of a meromorphic function // Abstract: It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function f(z), the relation m(r, (\Delta_c f - ac)/(f' - a))=S(r, f') holds, where \Delta_c f = f(z+c) - f(z), and where a and c are complex constants. As a consequence, for instance, it follows that if f is an entire function of sufficiently slow growth, whose derivative does not attain the complex value a often, i.e. N(r, 1/(f' - a)) = S(r, f), then the finite difference \Delta_c f cannot attain the value ac significantly more often, i.e. N(r, 1/(Delta_c f - ac))=S(r, f).