Abstract
We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series \(F(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n e^{z\lambda _n } }\) and \(B(z) = \sum\nolimits_{n = 0}^{ + \infty } {a_n b_n e^{z\lambda _n } }\) to be asymptotically equivalent as Re z → +∞ outside a certain set of finite measure.
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REFERENCES
A. M. Gaisin, “Estimate for the Dirichlet series with Fejer lacunas,” Dokl. Ros. Akad. Nauk, 370, No.6, 735–737 (2000).
O. B. Skaskiv, “On the behavior of the maximum term of a Dirichlet series that defines an entire function,” Mat. Zametki, 37, No.1, 41–47 (1985).
O. B. Skaskiv, “On some relations between the maximum of the modulus and the maximum term of the entire Dirichlet series,” Mat. Zametki, 56, No.2, 282–292 (1999).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 571–576, April, 2005.
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Skaskiv, O.B., Trakalo, O.M. On the Stability of the Maximum Term of the Entire Dirichlet Series. Ukr Math J 57, 686–693 (2005). https://doi.org/10.1007/s11253-005-0220-9
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DOI: https://doi.org/10.1007/s11253-005-0220-9