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Value distribution and linear operators

Halburd, R; Korhonen, R; (2013) Value distribution and linear operators.

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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.

Title:Value distribution and linear operators
Additional information:Accepted for publication in the Proceedings of the Edinburgh Mathematical Society
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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