Abstract
For entire Dirichlet series, we establish conditions on its coefficients and exponents under which the logarithms of the maximal term and of the maximum of the modulus are regularly varying functions of order ρ ∈ [1, + ∞) and the central exponent is a regularly varying function of order ρ − 1.
Similar content being viewed by others
REFERENCES
E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin–Heidelberg–New York, 1976.
N. V. Zabolotskii and M. N. Sheremeta, “On the slow growth of the main characteristics of entire functions,” Mat. Zametki [Math. Notes], 65 (1999), no. 2, 206–214.
O. B. Skaskiv and O. M. Trakalo, “On the slow growth of the numeric function of a given sequence,” Visnik Lviv. Nat. Univ. Ser. Mekh. Mat. (2000), no. 57, 36–40.
A. F. Leont'ev, Series of Exponentials [in Russian], Nauka, Moscow, 1976.
M. A. Evgrafov, Asymptotic Estimates and Entire Function [in Russian], Nauka, Moscow, 1979.
O. B. Skaskiv, “The maximum of the modulus and the maximal term of an entire Dirichlet series,” Dop. URSR. Ser. A (1984), no. 11, 22–24.
M. N. Sheremeta, “On the equivalence of the logarithms of the maximum of the modulus and of the maximal term of an entire Dirichlet series,” Mat. Zametki [Math. Notes], 42 (1987), no. 2, 215–226.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Filevich, P.V., Sheremeta, M.N. Regularly Increasing Entire Dirichlet Series. Mathematical Notes 74, 110–122 (2003). https://doi.org/10.1023/A:1025027418525
Issue Date:
DOI: https://doi.org/10.1023/A:1025027418525