Abstract
We establish new criteria of boundedness of the L-index along the direction for entire functions in ℂ n . These criteria are formulated as an estimate for the maximum modulus via the minimum modulus on a circle and also in terms of the restrictions imposed on the distribution of their zeros and on the behavior of the directional logarithmic derivative. In this way, we prove Hypotheses 1 and 2 from [A. I. Bandura and O. B. Skaskiv, Mat. Stud., 43, No. 1, 103–109 (2015)]. The obtained results are also new for the entire functions of bounded index and l-index in ℂ. They improve the well-known results by M. N. Sheremeta, A. D. Kuzyk, and G. H. Fricke.
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