Value distribution and linear operators

Rodney Halburd; Risto Korhonen

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arXiv · 1309.3333

Value distribution and linear operators

Rodney Halburd·Risto Korhonen

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Abstract

Nevanlinna's second main theorem is a far-reaching generalisation of Picard's Theorem concerning the value distribution of an arbitrary meromorphic function f. The theorem takes the form of an inequality containing a ramification term in which the zeros and poles of the derivative f' appear. In this paper we show that a similar result holds for special subfields of meromorphic functions where the derivative is replaced by a more general linear operator, such as higher-order differential operators and differential-difference operators. We subsequently derive generalisations of Picard's Theorem and the defect relations.

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Rodney Halburd, Risto Korhonen. 2013-09-12. Value distribution and linear operators. https://arxiv.org/abs/1309.3333

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