English

Meromorphic functions of finite $\varphi$-order and linear $q$-difference equations

Complex Variables 2020-10-26 v1

Abstract

The φ\varphi-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex plane are investigated in terms of the φ\varphi-order, which measures the growth of functions between the classical order and the logarithmic order. Several results on value distribution of meromorphic functions are discussed by using the φ\varphi-order and the φ\varphi-exponent of convergence. Instead of linear differential equations, the applications in the complex plane lie in linear qq-difference equations.

Keywords

Cite

@article{arxiv.2010.12356,
  title  = {Meromorphic functions of finite $\varphi$-order and linear $q$-difference equations},
  author = {Janne Heittokangas and Jun Wang and Zhi-Tao Wen and Hui Yu},
  journal= {arXiv preprint arXiv:2010.12356},
  year   = {2020}
}

Comments

28 pages

R2 v1 2026-06-23T19:35:17.819Z