Nevanlinna, Siegel, and Cremer
نویسندگان
چکیده
منابع مشابه
Nevanlinna, Siegel, and Cremer
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...
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Let f be a quadratic polynomial which has an irrationally indi erent xed point Let z be a biaccessible point in the Julia set of f Then In the Siegel case the orbit of z must eventually hit the critical point of f In the Cremer case the orbit of z must eventually hit the xed point Siegel polynomials with biaccessible critical point certainly exist but in the Cremer case it is possible that biac...
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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...
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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...
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Value distribution of a rational function f is controlled by its degree d, which is the number of preimages of a generic point. If we denote by n(a) the number of solutions of the equation f(z) = a, counting multiplicity, in the complex plane C, then n(a) ≤ d for all a ∈ C with equality for all a with one exception, namely a = f(∞). The number of critical points of f in C, counting multiplicity...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2004
ISSN: 0022-2518
DOI: 10.1512/iumj.2004.53.2503