Some improvements of criteria of Lindex boundedness in direction 

Author 
andriykopanytsia@gmail.com
IvanoFrankivsk National Technical University of Oil and Gas, IvanoFrankivsk, Ukraine

Abstract 
In this paper,
we improve criteria of boundedness of $L$index in direction for entire functions in $\mathbb{C}^n.$ They give an estimate of maximum modulus
on circles of various radius, maximum modulus by minimum modulus on circle and describe the behavior of directional logarithmic derivative and the distribution of zeros.
The obtained results are also new for entire functions of bounded index in $\mathbb{C}.$

Keywords 
entire function; bounded Lindex in direction; distribution of zeros; directional logarithmic derivative

DOI 
doi:10.15330/ms.47.1.2732

Reference 
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Pages 
2732

Volume 
47

Issue 
1

Year 
2017

Journal 
Matematychni Studii

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