Nevanlinna theory for the difference operator
| dc.creator | Halburd, R. G. | |
| dc.creator | Korhonen, R. J. | |
| dc.date | 2005-06-01 | |
| dc.date.accessioned | 2026-07-07T05:20:26Z | |
| dc.date.available | 2026-07-07T05:20:26Z | |
| dc.description | Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a theory for the exact difference $f\mapsto Δf=f(z+c)-f(z)$. An $a$-point of a meromorphic function $f$ is said to be $c$-paired at $z\in\C$ if $f(z)=a=f(z+c)$ for a fixed constant $c\in\C$. In this paper the distribution of paired points of finite-order meromorphic functions is studied. One of the main results is an analogue of the second main theorem of Nevanlinna theory, where the usual ramification term is replaced by a quantity expressed in terms of the number of paired points of $f$. Corollaries of the theorem include analogues of the Nevanlinna defect relation, Picard's theorem and Nevanlinna's five value theorem. Applications to difference equations are discussed, and a number of examples illustrating the use and sharpness of the results are given. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506011 | |
| dc.identifier | http://arxiv.org/abs/math/0506011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75380 | |
| dc.subject | Complex Variables | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 30D35 (primary) 39A10, 39A12 (secondary) | |
| dc.title | Nevanlinna theory for the difference operator | |
| dc.type | text |