On smoothly growing meromorphic functions (Q793184)

This paper concerns functions f meromorphic in the plane whose characteristic \(T(r,f)\) satisfies \(\lim_{r\to \infty}T(\lambda r,f)/T(r,f)=1.\) It extends previous results of the author, which will appear in J. Lond. Math. Soc. and Ann. Acad. Sci. Fenn. There are various technical results regarding the distribution of zeros and poles of f and f', the growth of the spherical derivative of f (in terms of T(r,f), \(\delta(\infty,f),\quad \Delta(\infty,f)),\) the ratio \(m(r,f)/m(r,f')\) and the deficiencies of f,f'. A number of the results are shown to be sharp.