On a Gross conjecture concerning entire functions of bounded index |
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| Author |
tftj@franko.lviv.ua
Faculty of Mechanics and Mathematics, Lviv National University
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| Abstract |
The following Gross conjecture is true: if an entire function $f$
is of unbounded index and $p$ is a polynomial, then the entire function
$F(z)=f(p(z))$ is of unbounded index.
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| Keywords |
Gross conjecture, polynomial, entire function, unbounded index
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| DOI |
doi:10.30970/ms.18.2.211-212
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Reference |
1. Sheremeta M. M. Analytic functions of bounded index, Lviv: VNTL Publishers, 1999, 141 pp.
2. Lepson B. Differential equations of infinite order, hyperdirichlet series and entire function of bounded index // Proc. Sympos. Pure Math. V.2. Amer. Math. Soc., Providence, Phode Island, 1968, 298–307. 3. Gross F. Entire functions of bounded index // Proc. Amer. Math. Soc. 18 (1967), 974–980. 4. Fricke G. H. A characterization of functions of bounded index // Indian J. Math. 14 (1972), № 3, 207–212. 5. Шеремета M. M. О целых функциях и рядах Дирихле ограниченного $l$-индекса, Изв. вузов. Матем. 9 (1992), № 9, 81--86. |
| Pages |
211-212
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| Volume |
18
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| Issue |
2
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| Year |
2002
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| Journal |
Matematychni Studii
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| Full text of paper | |
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