A proof of a Sheremeta conjecture concerning entire function of bounded $l$-index

Author
M.T. Bordulyak
Department of Mechanics and Mathematics, Lviv University,Univetrsytetska 1, 290602, Lviv, Ukraine
Abstract
We proved the Sheremeta conjecture on existence for entire function $f$ of bounded multiplicities of zeros a positive continuous on $[0;+\infty)$ function $ l$ such that $f$ is of bounded $l$-index.
Keywords
entire function, bounded multiplicities of zeros, positive continuous function, Sheremeta conjecture
DOI
doi:10.30970/ms.12.1.108-110
Reference
1. Kuzyk A.D., Sheremeta M.N. Entire functions of bounded $l$-distribution of values // Matem. zametki. -- 1986 V. 39 № 1 p. 3--13 (in Russian)

2. Gol'dberg A.A., Sheremeta M.N. On existence of entire transcendental function of bounded $l$-index // Matem. zametki. -- 1995 V. 57 № 1 p. 125--129 (in Russian)

3. Bordulyak M.T., Sheremeta M.M. On existence of entire functions of bounded $l$-index and $l$-regular growth // Ukr. matem. zh. -- 1996 V. 48 № 9 p. 1166--1182 (in Russian)

4. Sheremeta M.M. Five open problems in the theory of entire functions // Matem. studii. – 1996 V. 6 № p. 157–159 (in Ukrainian)

Pages
108-110
Volume
12
Issue
1
Year
1999
Journal
Matematychni Studii
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