Weighted discrete universality of the Riemann zeta-function
It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set. In the paper, we obtain a weighted discrete...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2020-01-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/10436 |
| _version_ | 1818791050686234624 |
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| author | Antanas Laurinčikas Darius Šiaučiūnas Gediminas Vadeikis |
| author_facet | Antanas Laurinčikas Darius Šiaučiūnas Gediminas Vadeikis |
| author_sort | Antanas Laurinčikas |
| collection | DOAJ |
| description | It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set. In the paper, we obtain a weighted discrete universality theorem for ζ(s) when τ takes values from the arithmetic progression {kh : k ∈N} with arbitrary fixed h > 0. For this, two types of h are considered. |
| first_indexed | 2024-12-18T15:05:11Z |
| format | Article |
| id | doaj.art-384d9b135fed46169328e5e8580d1f2d |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T15:05:11Z |
| publishDate | 2020-01-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-384d9b135fed46169328e5e8580d1f2d2022-12-21T21:03:47ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102020-01-0125110.3846/mma.2020.10436Weighted discrete universality of the Riemann zeta-functionAntanas Laurinčikas0Darius Šiaučiūnas1Gediminas Vadeikis2Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, LithuaniaInstitute of Regional Development, Šiauliai University, P. Višinskio str. 25, LT-76351, Šiauliai, LithuaniaInstitute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, LithuaniaIt is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set. In the paper, we obtain a weighted discrete universality theorem for ζ(s) when τ takes values from the arithmetic progression {kh : k ∈N} with arbitrary fixed h > 0. For this, two types of h are considered.https://journals.vgtu.lt/index.php/MMA/article/view/10436approximation of analytic functionsMergelyan theoremRiemann zeta-functionuniversalityweak convergence |
| spellingShingle | Antanas Laurinčikas Darius Šiaučiūnas Gediminas Vadeikis Weighted discrete universality of the Riemann zeta-function Mathematical Modelling and Analysis approximation of analytic functions Mergelyan theorem Riemann zeta-function universality weak convergence |
| title | Weighted discrete universality of the Riemann zeta-function |
| title_full | Weighted discrete universality of the Riemann zeta-function |
| title_fullStr | Weighted discrete universality of the Riemann zeta-function |
| title_full_unstemmed | Weighted discrete universality of the Riemann zeta-function |
| title_short | Weighted discrete universality of the Riemann zeta-function |
| title_sort | weighted discrete universality of the riemann zeta function |
| topic | approximation of analytic functions Mergelyan theorem Riemann zeta-function universality weak convergence |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/10436 |
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