Nevanlinna, Siegel, and Cremer Yusuke Okuyama 30D0530F3537F5039B12Nevanlinna theoryirrationally indifferent cycleSiegel cycleCremer cycle 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. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2503 10.1512/iumj.2004.53.2503 en Indiana Univ. Math. J. 53 (2004) 755 - 764 state-of-the-art mathematics http://iumj.org/access/