Abstract
The question is investigated of the coincidence on a ray and in a half-plane of generalized orders of growth of analytic functions represented by Dirichlet series absolutely convergent in the half-plane.
Similar content being viewed by others
Literature cited
A. F. Leont'ev, Sequences of Polynomials of Exponentials [in Russian], Nauka, Moscow (1980).
Yu Ghia Yung, “Sur la croissance de certaines series de Dirichlet sur des demi-droites horisontales,” C. R. Acad. Sci., Ser. 1,296, No. 4, 187–190 (1983).
V. M. Sorokivskii, “On the growth of analytic functions represented by Dirichlet series,” Ukr. Mat. Zh.,36, No. 4, 524–528 (1984).
A. M. Gaisin, “An estimation of the growth of a function represented by a Dirichlet series in a half-strip,” Mat. Sb.,117, No. 3, 412–424 (1982).
A. M. Gaisin, “The behavior of the sum of a Dirichlet series in half-strips,” Mat. Zametki,42, No. 5, 660–669 (1987).
Yu. M. Gal' and M. N. Sheremeta, “On the growth of functions analytic in a half-plane and defined by Dirichlet series,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1064–1067 (1978).
Yu. M. Gal', Asymptotic Porperties of Analytic Functions Defined by Dirichlet Series Absolutely Convergent in a Half-Plane [in Russian], Author's Abstract of Dissertation, Kiev (1986).
G. Pólya, “'Untersuchungen über Lücken und Singularitäten von Potenzreihen,” Mathematische Zeitschrift,29, 549–640 (1929).
A. J. Macintyre, “Asymptotic paths of integral functions with gap power series,” Proc. London Math. Soc.,2, 286–298 (1952).
M. N. Sheremeta, “Uniqueness theorems for Dirichlet entire series,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 64–72 (1987).
A. A. Gol'dberg and I. V. Ostrovskii, Distribution of the Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).
A. F. Leont'ev, Series of Exponentials [in Russian], Nauka, Moscow (1976).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 363–371, March, 1990.
Rights and permissions
About this article
Cite this article
Skaskiv, O.B., Sorokivskii, V.M. Growth of horizontal rays of analytic functions represented by Dirichlet series. Ukr Math J 42, 323–330 (1990). https://doi.org/10.1007/BF01057017
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01057017