JournalszaaVol. 21, No. 1pp. 265–272

Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen

  • Tomohiko Sato

    Osaka University, Japan
Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen cover
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Abstract

It is well known that, when f(z)f(z) is an entire function of order ρ\rho and ρ>\rho > \infty, then the limit lim suprT(r,f)T(r,f)_{r \rightarrow \infty} \frac{T(r,f')}{T(r,f)} is finite as rr \rightarrow \infty through all values or outside a set EE of finite measure. But for ρ=\rho = \infty, Hayman has shown that the assertion does not hold by constructing an entire function f(z)f(z) and an exceptional set EE of even infinite measure. In this paper, we will further extend his result to the case where f(z)f(z) is an algebroid function of order ρ=\rho = \infty.

Cite this article

Tomohiko Sato, Die Nevanlinna-Charakteristik von algebroiden Funktionen und ihren Ableitungen. Z. Anal. Anwend. 21 (2002), no. 1, pp. 265–272

DOI 10.4171/ZAA/1078