Lectures on Nevanlinna theory
نویسنده
چکیده
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, is at most 2d− 2. Nevanlinna theory generalizes these facts to transcendental functions f : C 7→ C. The main tool is the characteristic function Tf (r) which replaces the degree in the case when f is transcendental.
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