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On the Stability of the Maximum Term of the Dirichlet Series

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Abstract

We study the behavior of the maximum term of the modified Dirichlet series (with positive exponents), the sum of which is an entire function. For the class of the entire Dirichlet series defined by some convex majorant of growth, we prove a criterion for the equivalence of the logarithm of the maximum term of the original series and the logarithm of the maximum term of the modified series (Hadamard composition) on the asymptotic set. The corresponding problem of the stability of the maximum term for entire Dirichlet series of arbitrary growth has been studied by A.M. Gaisin (the first author) in connection with the Polya problem of the asymptotic behavior of entire transcendental functions on curves going to infinity.

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REFERENCES

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Funding

This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-02-2022-1826.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Science, 450008, Ufa, Bashkortostan, Russia

    A. M. Gaisin

  2. Bashkir State University, 450076, Ufa, Bashkortostan, Russia

    G. A. Gaisina

Authors
  1. A. M. Gaisin
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  2. G. A. Gaisina
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Corresponding authors

Correspondence to A. M. Gaisin or G. A. Gaisina.

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The authors declare that they have no conflicts of interest.

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Translated by L. Kartvelishvili

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Gaisin, A.M., Gaisina, G.A. On the Stability of the Maximum Term of the Dirichlet Series. Russ Math. 67, 20–29 (2023). https://doi.org/10.3103/S1066369X23010024

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  • DOI: https://doi.org/10.3103/S1066369X23010024

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