Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 17-30

A NEW PICARD TYPE THEOREM CONCERNING ELLIPTIC FUNCTIONS

Qiaoyu Chen, Xuecheng Pang and Pai Yang

Shanghai Lixin University of Commerce, School of Mathematics and Information Science
Shanghai 201620, P.R. China; goodluckqiaoyu 'at' 126.com

East China Normal University, Department of Mathematics
Shanghai 200241, P.R. China; xcpang 'at' math.ecnu.edu.cn

Chengdu University of Information Technology, College of Applied Mathematics
Chengdu 610225, P.R. China; yangpai 'at' cuit.edu.cn

Abstract. Let k ≥ 2 be an integer, let h be a nonconstant elliptic function, and let f be a nonconstant meromorphic function in C, all of whose zeros have multiplicity at least k + 1, except possibly finitely many. If T(r,h) = o{T(r,f)} as r → ∞, then f(k) = h has infinitely many solutions (including the possibility of infinitely many common poles of f and h).

2010 Mathematics Subject Classification: Primary 30D35, 30D45.

Key words: Meromorphic function, elliptic function, normal family.

Reference to this article: Q. Chen, X. Pang and P. Yang: A new Picard type theorem concerning elliptic functions. Ann. Acad. Sci. Fenn. Math. 40 (2015), 17-30.

Full document as PDF file

doi:10.5186/aasfm.2015.4001