A weighted version of the Mishou theorem

A weighted version of the Mishou theorem

In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R. In the paper, the Mishou theorem is generalized for the set of...

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Main Authors: Antanas Laurinčikas, Darius Šiaučiūnas, Gediminas Vadeikis
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2021-01-01
Series:Mathematical Modelling and Analysis
Subjects:
hurwitz zeta-function
mishou theorem
riemann zeta-function
universality
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/12445
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spelling doaj-d1fdb0b7987d4e9f808f722c1f4d7aa52021-07-02T20:22:53ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102021-01-01261213310.3846/mma.2021.1244512445A weighted version of the Mishou theoremAntanas Laurinčikas0Darius Šiaučiūnas1Gediminas Vadeikis2Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, LithuaniaInstitute of Regional Development, Šiauliai University, P. Višinskio g. 25, LT-76351 Šiauliai, LithuaniaInstitute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko g. 24, LT-03225 Vilnius, LithuaniaIn 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R. In the paper, the Mishou theorem is generalized for the set of above shifts having a weighted positive lower density. Also, the case of a positive density is considered.https://journals.vgtu.lt/index.php/MMA/article/view/12445hurwitz zeta-functionmishou theoremriemann zeta-functionuniversality
collection DOAJ
language English
format Article
sources DOAJ
author Antanas Laurinčikas
Darius Šiaučiūnas
Gediminas Vadeikis
spellingShingle Antanas Laurinčikas
Darius Šiaučiūnas
Gediminas Vadeikis
A weighted version of the Mishou theorem
Mathematical Modelling and Analysis
hurwitz zeta-function
mishou theorem
riemann zeta-function
universality
author_facet Antanas Laurinčikas
Darius Šiaučiūnas
Gediminas Vadeikis
author_sort Antanas Laurinčikas
title A weighted version of the Mishou theorem
title_short A weighted version of the Mishou theorem
title_full A weighted version of the Mishou theorem
title_fullStr A weighted version of the Mishou theorem
title_full_unstemmed A weighted version of the Mishou theorem
title_sort weighted version of the mishou theorem
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2021-01-01
description In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R. In the paper, the Mishou theorem is generalized for the set of above shifts having a weighted positive lower density. Also, the case of a positive density is considered.
topic hurwitz zeta-function
mishou theorem
riemann zeta-function
universality
url https://journals.vgtu.lt/index.php/MMA/article/view/12445
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