On the Regular Behavior of Entire Functions of Zero Order along Curves of Regular Rotation
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 537-549.

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We study the relationship between the existence of an $\upsilon$-density $\Delta^\gamma (\alpha,\beta)$ of roots along the curves of regular rotation of an entire function of zero order and the regular behavior at infinity of its logarithm.
Keywords: entire function, zero order, curve of regular rotation, logarithm, density of roots.
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N. V. Zabolotskii; M. R. Mostova; V. E. Shvets. On the Regular Behavior of Entire Functions of Zero Order along Curves of Regular Rotation. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 537-549. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a4/

[1] A. Macintyre, “Laplace's transformation and integral functions”, Proc. London Math. Soc. (2), 45:2 (1938), 1–20 | MR

[2] P. Kennedy, “A class of integral functions bounded on certain curves”, Proc. London Math. Soc., 3:6 (1956), 518–547 | DOI | MR

[3] S. K. Balashov, “O tselykh funktsiyakh konechnogo poryadka s kornyami na krivykh pravilnogo vrascheniya”, Izv. AN SSSR. Ser. matem., 37:3 (1973), 603–629 | MR | Zbl

[4] A. I. Kheifits, “Analog teoremy Valirona–Titchmarsha dlya tselykh funktsii s kornyami na logarifmicheskoi spirali”, Izv. vuzov. Matem., 1980, no. 12, 74–75 | MR | Zbl

[5] S. K. Balashov, “O funktsiyakh vpolne regulyarnogo rosta po krivym pravilnogo vrascheniya”, Izv. AN SSSR. Ser. matem., 40:2 (1976), 338–354 | MR | Zbl

[6] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956 | MR | Zbl

[7] N. V. Zabolotskii, “Silno regulyarnyi rost tselykh funktsii nulevogo poryadka”, Matem. zametki, 63:2 (1998), 196–208 | DOI | MR | Zbl

[8] M. V. Zabolotskii, “An example of entire function of strongly regular growth”, Mat. Stud., 13:2 (2000), 145–148 | MR

[9] A. A. Goldberg, I. V. Ostrovskii, Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR | Zbl

[10] M. Zabolotskyi, Yu. Basiuk, “Proximity of the entire functions of zero order with $\upsilon$-density of zeros”, Visnyk of the Lviv Univ. Series Mech. Math., 84 (2017), 80–86 http://nbuv.gov.ua/UJRN/VLNU_Mech_mat_2017_84_13