Value distribution of meromorphic functions concerning rational functions and differences

Abstract

Abstract Let c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of f − R $f-R$ , its shift f ( z + n c ) $f(z+nc)$ and the differences Δ c n f $\Delta _{c}^{n} f$ .

Keywords

• Meromorphic functions
• Value distribution
• Rational functions
• Differences