Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function. II

被引：0
作者：
Renata Macaitienė
Darius Šiaučiūnas
机构：
[1] Institute of Regional Development,
[2] Šiauliai Academy,undefined
[3] Vilnius University,undefined
来源：
Lithuanian Mathematical Journal | 2021年 / 61卷
关键词：
Hurwitz zeta-function; nontrivial zeros; Riemann zeta-function; space of analytic functions; universality; 11M06; 11M41;
D O I：
暂无
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学科分类号：
摘要：
Let 0 < γ1 < ⋯ ≤ γk ≤ ⋯ be the sequence of imaginary parts of nontrivial zeros of the Riemann zetafunction. In [R. Macaitienė and D. Šiaučiūnas, Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function, Lith. Math. J., 59(1):81–95, 2019] a joint universality theorem on the approximation of analytic functions by shifts of the Hurwitz zeta-functions ζ(s + ihγk, α1), …, ζ(s + ihγk, αr) has been obtained. In the paper, we prove universality theorems for the compositions F(ζ(s + ihγk, α1), …, ζ(s + ihγk, αr)) for some classes of operators in the r-dimensional space of analytic functions.
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页码：382 / 390
页数：8
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共 23 条
[1]  
Buivydas E(2015)A discrete version of the Mishou theorem Ramanujan J. 38 331-347
[2]  
Laurinčikas A(2016)Distribution modulo 1 and the discrete universality of the Riemann zeta-function Abh. Math. Semin. Univ. Hamb. 86 79-87
[3]  
Dubickas A(2018)The Riemann hypothesis and universality of the Riemann zeta-function Math. Slovaca 68 741-748
[4]  
Laurinčikas A(2017)Zeros of the Riemann zeta-function and its universality Acta Arith. 181 127-142
[5]  
Garunkštis R(2019)A new application of the Gram points Aequationes Math. 93 859-873
[6]  
Laurinčikas A(2020)A new application of the Gram points. II Aequationes Math. 94 1171-1187
[7]  
Garunkštis R(2010)Universality of the Riemann zeta-function J. Number Theory 130 2323-2331
[8]  
Laurinčikas A(2013)On the universality of the Hurwitz zeta-function Int. J. Number Theory 9 155-165
[9]  
Macaitienė R(2014)Joint discrete universality of Hurwitz zeta-functions Sb. Math. 205 1599-1619
[10]  
Korolev M(2020)Zeros of the Riemann zeta-function in the discrete universality of the Hurwitz zeta-function Stud. Sci. Math. Hung. 57 147-164
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