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The frequency of the zeros of the difference of a solution to a linear differential equation and a small function. (English) Zbl 1212.34279

Summary: We estimate the exponent of convergence of the zeros of \(f^{(l)}-g\), where \(f\) is the solution of a \(k\)-th \((l\leq k)\) order linear differential equation and \(g\) is a small function. By setting \(g(z)=z\) and \(l=0\), we obtain some new results on the fixed points of such solutions.

MSC:

34M03 Linear ordinary differential equations and systems in the complex domain
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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