Binomial asymptotics for the logarithmic derivative of zero-order entire functions with zeros along curves of regular rotation |
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| Author |
mykola.zabolotskyy@lnu.edu.ua1, yuliya.basyuk.92@gmail.com2, mariana.mostova@gmail.com3
1) Ivan Franko National University of Lviv,
Lviv, Ukraine; 2) Ivan Franko National University of Lviv,
Lviv, Ukraine; 3) Ivan Bobersky Lviv State University of Physical Culture,
Lviv, Ukraine
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| Abstract |
The relationship between the regular behavior of the logarithmic derivative of zero-order entire function $f$ with zeros on
a finite system of curves of regular rotation for $f$ and the existence of $\upsilon$-density of zeros of $f$ along such curves
is investigated.
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| Keywords |
logarithmic derivative; entire function; order zero; binomial asymptotics; curves of regular rotation
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| DOI |
doi:10.30970/ms.52.2.156-165
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| Reference |
1. S.K. Balashov, On entire functions of completely regular growth along curves of regular rotation, Math.
USSR Izv., 10 (1976), ¹2, 321–338. doi:10.1070/IM1976v010n02ABEH001691; translation of Izv. Akad.
Nauk SSSR Ser. Mat., 40 (1976), ¹2, 338–354. (in Russian)
2. S.K. Balashov, On entire functions of finite order with zeros on curves of regular rotation, Math. USSR Izv., 7 (1973), ¹3, 601–627. doi:10.1070/IM1973v007n03ABEH001963; translation of Izv. Akad. Nauk SSSR Ser. Mat., 37 (1973), ¹3, 603–629. (in Russian) 3. A.A. Goldberg, N.E. Korenkov, Asymptotic behavior of logarithmic derivative of entire function of completely regular growth, Sib. Math. J., 21 (1980), ¹3, 363–375. doi:10.1007/BF00968180; translation of Sibirsk. Mat. Zh., 21 (1980), ¹3, 63–79. (in Russian) 4. A.A. Goldberg, I.V. Ostrovskii, Value distribution of meromorphic functions, Nauka, Moscow, 1970. (in Russian) 5. A.A. Goldberg, N.N. Strochik, Asymptotic behavior of meromorphic functions of completely regular growth and of their logarithmic derivatives, Sib. Math. J., 26 (1985), ¹6, 802–809. doi:10.1007/BF00969100; translation of Sibirsk. Mat. Zh., 26 (1985), ¹6, 29–38. (in Russian) 6. A.A. Goldberg, N.V. Zabolotskii, Concentration index of a subharmonic function of zeroth order, Math. Notes, 34 (1983), ¹2, 596–601. doi:10.1007/BF01141775; translation of Mat. Zametki, 34 (1983), ¹2, 227–236. (in Russian) 7. M.V. Zabolotskii, Valiron-type and Valiron–Titchmarsh-type theorems for entire functions of order zero, Ukrainian Math. J., 48 (1996), ¹3, 354–366. doi:10.1007/BF02378526; translation of Ukrain. Mat. Zh., 48 (1996), ¹3, 315–325. (in Ukrainian) 8. N.V. Zabolotskii, Strongly regular growth of entire functions of order zero, Math. Notes, 63 (1998), ¹2, 172–182. doi:10.1007/BF02308756; translation of Mat. Zametki, 63 (1998), ¹2, 196–208. doi:10.4213/mzm1266 (in Russian) 9. M.V. Zabolotskyi, Yu.V. Basyuk, S.I. Tarasyuk, Entire functions of order zero with zeros on a logarithmic spiral, Ukrainian Math. J., 70 (2018), ¹7, 1063–1074. doi:10.1007/s11253-018-1552-6; translation of Ukrain. Mat. Zh., 70 (2018), ¹7, 923–932. (in Ukrainian) 10. M.V. Zabolotskyi, M.R. Mostova, Sufficient conditions for the existence of the v-density of zeros for an entire function of order zero, Ukrainian Math. J., 68 (2016), ¹4, 570–582. doi:10.1007/s11253-016-1242- 1; translation of Ukrain. Mat. Zh., 68 (2016), ¹4, 506–516. (in Ukrainian) 11. M.V. Zabolotskyj, M.R. Mostova, Asymptotic behavior of the logarithmic derivative of entire functions of zero order, Carpathian Math. Publ., 6 (2014), ¹2, 237–241. doi:10.15330/cmp.6.2.237-241 (in Ukrainian) |
| Pages |
156-165
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| Volume |
52
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| Issue |
2
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| Year |
2019
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |