Directional logarithmic derivative and the distribution of zeros of an entire function of bounded $L$-index in the direction
AbstractWe establish new criteria of boundedness of the $L$-index in the direction for entire functions in $C^n$. These criteria are formulated as estimate of the maximum modulus via the minimum modulus on a circle and describe the distribution of their zeros and the behavior of the directional logarithmic derivative. In this way, we prove Hypotheses 1 and 2 from the article [Bandura A. I., Skaskiv O. B. Open problems for entire functions of bounded index in direction // Mat. Stud. – 2015. – 43, № 1. – P. 103 – 109]. The obtained results are also new for the entire functions of bounded index in $C$. They improve the known results by M. N. Sheremeta, A. D. Kuzyk, and G. H. Fricke.
How to Cite
BanduraA. І., and SkaskivO. B. “Directional Logarithmic Derivative and the Distribution of Zeros of an Entire Function of Bounded $L$-Index in the Direction”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 3, Mar. 2017, pp. 426-32, http://umj.imath.kiev.ua/index.php/umj/article/view/1706.