Entire functions of bounded L-index: its zeros and behavior of partial logarithmic derivatives
Summary: In this paper, we obtain new sufficient conditions of boundedness of \(\mathbf{L}\)-index in joint variables for entire function in \(\mathbb{C}^n\) functions. They give an estimate of maximum modulus of an entire function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives and the distribution of zeros. In some sense, the obtained results are new for entire functions of bounded index and \(l\)-index in \(\mathbb{C}\) too. They generalize known results of Fricke, Sheremeta, and Kuzyk.
scientific article; zbMATH DE number 6945693
scientific article