Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 923-946

TROPICAL VARIANTS OF SOME COMPLEX ANALYSIS RESULTS

Ilpo Laine, Kai Liu and Kazuya Tohge

University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, FI-80101, Finland; ilpo.laine 'at' uef.fi

Nanchang University, Department of Mathematics
Nanchang, Jiangxi, 330031, P.R. China; liukai 'at' ncu.edu.cn

Kanazawa University, College of Science and Engineering
Kanazawa 920-1192, Japan; tohge 'at' se.kanazawa-u.ac.jp

Abstract. Tropical Nevanlinna theory studies value distribution of continuous piecewise linear functions of a real variable. In this paper, we use the reasoning from tropical Nevanlinna theory to present tropical counterparts of some classical complex results related to Fermat type equations, Hayman conjecture and Brück conjecture.

2010 Mathematics Subject Classification: Primary 39A12, 30D30.

Key words: Tropical meromorphic functions, tropical Nevanlinna theory, Fermat type equations, Hayman conjecture, Brück conjecture.

Reference to this article: I. Laine, K. Liu and K. Tohge: Tropical variants of some complex analysis results. Ann. Acad. Sci. Fenn. Math. 41 (2016), 923-946.

Full document as PDF file

doi:10.5186/aasfm.2016.4159