On a problem of Hayman
Let f be a transcendental meromorphic function in the plane, let k be a positive integer and p a nonzero polynomial. Then the author proves that for any \(\epsilon >0\) \[ T(r,f)\leq (1+(1/k)+\epsilon)\{N(r,1/f)+N(r,1/(f^{(k)}-p))\}+S(r,f), \] where S(r,f) depends on \(\epsilon\). This improves a result of \textit{W. K. Hayman} [Ann. Math., II. Ser. 70, 9-42 (1959; Zbl 0088.285)].
scientific article; zbMATH DE number 4175344