On a Dirichlet Series Connected to a Periodic Hurwitz Zeta-Function With Transcendental and Rational Parameter

Balčiūnas, Aidas; Laurinčikas, Antanas; Stoncelis, Mindaugas

doi:10.3846/mma.2023.17222

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2024

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“…A generalization of the above results for ζ u T (s; a) with multiplicative sequence a was presented in [9] and [10]. Similar problems for ζ u T (s, α; {1}) and ζ u T (s, α; b) were discussed in [26] and [5]. The papers [22] and [24] are devoted to extension of Mishou's theorem for absolutely convergent Dirichlet series.…”

Section: Introductionmentioning

confidence: 85%

A Discrete Version of the Mishou Theorem Related to Periodic Zeta-Functions

Balčiūnas,

Jasas,

Rimkevičienė

2024

Mathematical Modelling and Analysis

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In the paper, we consider simultaneous approximation of a pair of analytic functions by discrete shifts $\zeta_{u_N}(s+ikh_1; \ga)$ and $\zeta_{u_N}(s+ikh_2, \alpha; \gb)$ of the absolutely convergent Dirichlet series connected to the periodic zeta-function with multiplicative sequence $\ga$, and the periodic Hurwitz zeta-function, respectively. We suppose that $u_N\to\infty$ and $u_N\ll N^2$ as $N\to\infty$, and the set $\{(h_1\log p:\! p\in\! \PP), (h_2\log(m+\alpha): m\in \NN_0), 2\pi\}$ is linearly independent over $\QQ$.

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