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This article is cited in 1 scientific paper (total in 1 paper)
Joint Universality of Certain Dirichlet Series
V. Garbaliauskienėa, D. Siauciunas a Institute for Regional Development, Šiauliai Academy, Vilnius University
Abstract:
In this paper, we define the Dirichlet series $ \zeta_{u_T j} (s)$, $ j = 1, \dots, r$, absolutely converging in the half-plane $ \operatorname{Re} s> 1/2 $ and prove that the set of shifts $ (\zeta_{u_T 1} (s + ia_1 \tau), \dots, \zeta_{u_T r} (s + ia_r \tau)) $ approximating a given set of analytic functions has a positive density on the interval $ [T, T + H]$, $ H = o (T) $ as $ T \to \infty$. Here $ a_1, \dots, a_r \in \mathbb{R} $ are algebraic numbers linearly independent over $ \mathbb{Q} $ and $ u_T \to \infty $ as $ T \to \infty$.
Keywords:
Riemann zeta function, Voronin's theorem, universality.
Received: 23.08.2021
Citation:
V. Garbaliauskienė, D. Siauciunas, “Joint Universality of Certain Dirichlet Series”, Mat. Zametki, 111:1 (2022), 15–23; Math. Notes, 111:1 (2022), 13–19
Linking options:
https://www.mathnet.ru/eng/mzm13222https://doi.org/10.4213/mzm13222 https://www.mathnet.ru/eng/mzm/v111/i1/p15
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Abstract page: | 173 | Full-text PDF : | 21 | References: | 41 | First page: | 14 |
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