Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 305-312

WIMAN-VALIRON THEOREM FOR q-DIFFERENCES

Zhi-Tao Wen and Zhuan Ye

Taiyuan University of Technology, Department of Mathematics
No. 79 Yingze West Street, Taiyuan, 030024, P.R. China; zhitaowen 'at' gmail.com

Taiyuan University of Technology, Taiyuan, 030024, P.R. China, and
Northern Illinois University, Department of Mathematical Sciences
DeKalb, IL 60115, U.S.A.; zye 'at' niu.edu

Abstract. Let q be any complex number other than 0 and 1. We first asymptotically express the logarithmic q-difference log f(qz) - log f(z) in terms of the logarithmic derivative f'/f for any meromorphic function f of order strictly less than 1/2. Then we show the assumption that the order strictly less than 1/2 is sharp. Finally, we prove a q-difference analogue of the Wiman-Valiron theorem for entire functions of order strictly less than 1/2.

2010 Mathematics Subject Classification: Primary 30D30, 30D05, 39B32.

Key words: Meromorphic functions, order, q-difference, Wiman-Valiron theorem.

Reference to this article: Z.-T. Wen and Z. Ye: Wiman-Valiron theorem for q-differences. Ann. Acad. Sci. Fenn. Math. 41 (2016), 305-312.

Full document as PDF file

doi:10.5186/aasfm.2016.4118