IUMJ

Title: Nevanlinna, Siegel, and Cremer

Authors: Yusuke Okuyama

Issue: Volume 53 (2004), Issue 3, 755-764

Abstract:

We study an irrationally indifferent cycle of points or circles of a rational function, which is either Siegel or Cremer by definition. We give a clear interpretation of some Diophantine quantity associated with an irrationally indifferent cycle as a quantity arising in the Nevanlinna theory. As a consequence, we show that an irrationally indifferent cycle is Cremer if this Nevanlinna-theoretical quantity does not vanish.