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Value distribution and linear operators

Halburd, R; Korhonen, R; 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.

Type: Article
Title: Value distribution and linear operators
Additional information: Accepted for publication in the Proceedings of the Edinburgh Mathematical Society
Keywords: math.CV, math.CV, Primary 30D35, Secondary 34M03, 34M05, 39A06
UCL classification: UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1335802
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