We study an irrationally indifferent cycle of points or circles of a rational function, which is either Siegel or Cremer by definition. We invent a new argument from the viewpoint of the Nevanlinna theory. Using this argument, we give a clear interpretation of some Diophantine quantity associated with an irrationally indifferent cycle. This quantity turns out to be Nevanlinnatheoretical. As a c...

It is well known that analytic interpolation theory has found various applications in systems and control, e.g., H∞ control, covariance extension problem for spectral estimation, filtering and gain equalization. For the engineering point of views, it is desirable to synthesize interpolants with bounded degree, where the interpolants correspond to the transfer functions, representing devices of ...

S. Lang [L] conjectured in 1974 that a hyperbolic algebraic variety defined over a number field has only finitely many rational points, and its analogue over function fields. We discuss the Nevanlinna-Cartan theory over function fields of arbitrary dimension and apply it for Diophantine property of hyperbolic projective hypersurfaces (homogeneous Diophantine equations) constructed by Masuda-Nog...

Nevanlinna theory [Ne] was created to give a quantitative measure of the value distribution for meromorphic functions, for instance to measure the extent to which they approximate a finite number of points. We view a meromorphic function as a holomorphic map ƒ : C —• P into the projective line. The theory has various higher dimensional analogues, of which we shall later consider maps ƒ : C —• X...

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging t...

As observed originally by C. Osgood, certain statements in value distribution theory bear a strong resemblance to certain statements in diophantine approximation, and their corollaries for holomorphic curves likewise resemble statements for integral and rational points on algebraic varieties. For example, if X is a compact Riemann surface of genus > 1, then there are no non-constant holomorphic...