Rad HAZU, Matematičke znanosti, Vol. 24 (2020), 99-116.

ESTIMATES OF THE LOGARITHMIC DERIVATIVE NEAR A SINGULAR POINT AND APPLICATIONS

Saada Hamouda

Abstract.   In this paper, we will give estimates near z = 0 for the logarithmic derivative | f ^(k)(z) / f(z) | where f is a meromorphic function in a region of the form D(0,R) = {z ∈ C : 0 < |z| < R}. Some applications on the growth of solutions of linear differential equations near a singular point are given.

2020 Mathematics Subject Classification.   34M10, 30D35.

Key words and phrases.   Logarithmic derivative estimates, Nevanlinna theory, linear differential equations, growth of solutions, singular point.

DOI: https://doi.org/10.21857/m3v76teqny

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