Value Distribution Theory of Holomorphic Functions

In mathematics, the value distribution theory of holomorphic functions is a division of mathematical analysis. It tries to get quantitative measures of the number of times a function f(z) assumes a value a, as z grows in size, refining the Picard theorem on behaviour close to an essential singularity. The theory exists for analytic functions (and meromorphic functions) of one complex variable z, or of several complex variables.

In the case of one variable the term Nevanlinna theory, after Rolf Nevanlinna, is also common. The now-classical theory received renewed interest, when Paul Vojta suggested some analogies with the problem of integral solutions to Diophantine equations. These turned out to involve some close parallels, and to lead to fresh points of view on the Mordell conjecture and related questions.


Famous quotes containing the words distribution, theory and/or functions:

    My topic for Army reunions ... this summer: How to prepare for war in time of peace. Not by fortifications, by navies, or by standing armies. But by policies which will add to the happiness and the comfort of all our people and which will tend to the distribution of intelligence [and] wealth equally among all. Our strength is a contented and intelligent community.
    Rutherford Birchard Hayes (1822–1893)

    No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.
    André Gide (1869–1951)

    In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.
    Urie Bronfenbrenner (b. 1917)