Stability of the Maximal Term of a Dirichlet Series of a Given Growth on a Discrete Set

G. A. Gaisina

Ufa University of Science and Technology

Abstract: For a Dirichlet series with positive exponents summable to an entire function, the behavior of the maximal term is studied. For the class of integer Dirichlet series whose growth is controlled by a convex majorant on some sequence of points, we prove a theorem on equivalence of the logarithms of the original series and the modified Dirichlet series on an asymptotic set.

Keywords: maximal term Dirichlet series, growth majorant, Hadamard composition, Young transform.

UDC: 517

Received: 16.06.2024
Revised: 19.09.2024

DOI: 10.4213/mzm14413

 English version: Mathematical Notes, 2025, 118:1, 48–59

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