Joint Universality of Certain Dirichlet Series
Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 15-23
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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.
@article{MZM_2022_111_1_a2,
author = {V. Garbaliauskien\.{e} and D. Siauciunas},
title = {Joint {Universality} of {Certain} {Dirichlet} {Series}},
journal = {Matemati\v{c}eskie zametki},
pages = {15--23},
publisher = {mathdoc},
volume = {111},
number = {1},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a2/}
}
V. Garbaliauskienė; D. Siauciunas. Joint Universality of Certain Dirichlet Series. Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 15-23. http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a2/