Abstract
Under consideration is a Dirichlet series depending on a parameter and absolutely convergent in the right half of the critical strip. We prove that the set of shifts of the series approximating a prescribed analytic function without zeros has positive density on the intervals of type \( [T,T+H] \), where \( T^{1/3}(\log T)^{26/15}\leq H\leq T \), and give this density explicitly.
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Funding
The research was funded by the European Social Fund according to the activity “Improvement of Researchers’ Qualification by Implementing World-Class R&D Projects” (Grant 09.3.3–LMT–K–712–01–0037).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 6, pp. 1330–1338. https://doi.org/10.33048/smzh.2021.62.609
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Laurinčikas, A. The Universality of an Absolutely Convergent Series on Short Intervals. Sib Math J 62, 1076–1083 (2021). https://doi.org/10.1134/S0037446621060094
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DOI: https://doi.org/10.1134/S0037446621060094