For entire functions whose zero counting functions are slowly increasing, we establish criteria for the regular growth of their logarithms of moduli and arguments in the metric of L p[0, 2π].
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References
E. Seneta, Regularly Varying Functions [Russian translation], Nauka, Moscow (1985).
A. A. Kondratyuk, Fourier Series and Meromorphic Functions [in Ukrainian], Vyshcha Shkola, Lviv (1988).
Ya. V. Vasyl’kiv, “Asymptotic behavior of the logarithmic derivative and logarithms of meromorphic functions of completely regular growth in the metric of L p[0, 2π] . 4.1,” Mat. Stud., 12, No. 1, 37–58 (1959).
Ya. V. Vasyl’kiv, “Asymptotic behavior of the logarithmic derivative and logarithms of meromorphic functions of completely regular growth in the metric of L p[0, 2π] . 4.2,” Mat. Stud., 12, No. 2, 135–144 (1959).
R. Z. Kalynets’ and A. A. Kondratyuk, “On the regularity of the growth of the modulus and argument of an entire function in the metric of L [0, 2π] p ,” Ukr. Mat. Zh., 50, No. 7, 889–896 (1998).
A. V. Bratishchev, “On the inversion of the l’Hospital rule,” in: Mechanics of Continuum [in Russian], Rostov University, Rostov-on-Don (1985), pp. 28–42.
M. V. Zabolotskii, “An example of an entire function of strongly regular growth,” Mat. Stud., 13, No. 2, 145–148 (2000).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 885–893, July, 2010.
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Bodnar, O.V., Zabolots’kyi, M.V. Criteria for the regularity of growth of the logarithm of modulus and the argument of an entire function. Ukr Math J 62, 1028–1039 (2010). https://doi.org/10.1007/s11253-010-0411-x
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DOI: https://doi.org/10.1007/s11253-010-0411-x