Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 523-549

DIFFERENCE ANALOGUE OF CARTAN'S SECOND MAIN THEOREM FOR SLOWLY MOVING PERIODIC TARGETS

Risto Korhonen, Nan Li and Kazuya Tohge

University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, 80101 Joensuu, Finland; risto.korhonen 'at' uef.fi

University of Jinan, School of Mathematical Sciences, Jinan, Shandong, 250022, P.R. China;
and University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, 80101 Joensuu, Finland; nanli32787310 'at' 163.com

Kanazawa University, School of Electrical and Computer Engineering
Kakuma-machi, Kanazawa, 920-1192, Japan; tohge 'at' se.kanazawa-u.ac.jp

Abstract. We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As applications, we obtain a new Picard type theorem and difference analogues of the deficiency relation for holomorphic curves.

2010 Mathematics Subject Classification: Primary 32H30; Secondary 30D35.

Key words: Entire function, meromorphic function, holomorphic curve, Casorati determinant, Nevanlinna theory, Cartan's second main theorem.

Reference to this article: R. Korhonen, N. Li and K. Tohge: Difference analogue of Cartan's second main theorem for slowly moving periodic targets. Ann. Acad. Sci. Fenn. Math. 41 (2016), 523-549.

Full document as PDF file

doi:10.5186/aasfm.2016.4131