On a conjecture of F. Nevanlinna concerning deficient function. II (Q913984)

[For part I see the authors in ibid., Ser. A 10, No.1, 1-7 (1989; reviewed above).] \textit{F. Nevanlinna} [Septième Congrès Math. Scand. Oslo 1930, 68-80 (1930)] conjectured that if a meromorphic function g(z) of order \(\rho \in (0,+\infty)\) stisfies \(\sum_{\ell}\delta (a_{\ell},g)=2,\) then each of the deficiencies is equal to \(n_{\ell}/\rho\) \((n_{\ell}\in {\mathfrak N})\). Let f(z) be an entire function of lower order \(\mu =(0,+\infty)\), let \(a_{\ell}(z)\) (\(\not\equiv \infty)\) be meromorphic functions with \(T(r,a_{\ell}(z))=o\{T(r,f)\}.\) In this paper, the authors prove that if \(\sum_{\ell}\delta (a_{\ell}(z),f)=1\), then the deficiencies \(\delta (a_{\ell}(z),f)\) are equal to \(n_{\ell}/\mu\) \((n_{\ell}\in {\mathfrak N})\).