Joint weighted universality of the Hurwitz zeta-functions

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-05-05 DOI:10.1090/spmj/1712

A. Laurinčikas, G. Vadeikis

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引用次数: 1

Abstract

Joint weighted universality theorems are proved concerning simultaneous approximation of a collection of analytic functions by a collection of shifts of Hurwitz zeta-functions with parameters α 1 , … , α r \alpha _1,\dots ,\alpha _r . For this, linear independence is required over the field of rational numbers for the set { log ⁡ ( m + α j ) : m ∈ N 0 = N ∪ { 0 } , j = 1 , … , r } \{\log (m+\alpha _j)\,:\, m\in \mathbb {N}_0=\mathbb {N}\cup \{0\},\;j=1,\dots ,r\} .

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Hurwitz函数的联合加权通用性

通过参数为α1，…，αr\α_1，\dots，\alpha_r的Hurwitzζ函数的一组移位，证明了关于一组解析函数的同时逼近的联合加权普遍性定理。为此，集合{log的有理数域上需要线性独立性⁡ （m+αj）：m∈N 0=Nõ｛0｝，j=1，…，r｝\｛\log（m+\alpha_j）\，：\，m\in\mathbb{N}_0=\mathbb｛N｝\cup \｛0\｝，\；j=1，\dots，r\｝。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.