Joint Discrete Approximation of a Pair of Analytic Functions by Periodic Zeta-Functions

被引：7

作者：

Balciunas, Aidas ^{[1
]}

Garbaliauskiene, Virginija ^{[2
]}

Karaliunaite, Julija ^{[3
]}

Macaitiene, Renata ^{[2
]}

Petuskinaite, Jurgita ^{[1
]}

Rimkeviciene, Audrone ^{[4
]}

机构：

[1] Vilnius Univ, Fac Math & Informat, Naugarduko Str 24, LT-03225 Vilnius, Lithuania

[2] Siauliai Univ, Inst Reg Dev, P Visinskio Str 25, LT-76351 Shiauliai, Lithuania

[3] Vilnius Gediminas Tech Univ, Fac Fundamental Sci, Sauletekio Av 11, LT-10223 Vilnius, Lithuania

[4] Siauliai State Coll, Fac Business & Technol, Ausros Av 40, LT-76241 Shiauliai, Lithuania

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2020年 / 25卷 / 01期

关键词：

Hurwitz zeta-function; non-trivial zeros of the Riemann zeta-function; periodic zeta-function; periodic Hurwitz zeta-function; universality; UNIVERSALITY THEOREM; NONTRIVIAL ZEROS; RIEMANN;

D O I：

10.3846/mma.2020.10450

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

引用

页码：71 / 87

页数：17

共 35 条

[1] [Anonymous], 1974, UNIFORM DISTRIBUTION
[2] Billingsley P, 2013, CONVERGE PROBAB MEAS
[3] On Approximation of Analytic Functions by Periodic Hurwitz Zeta-Functions
Franckevic, Violeta
Laurincikas, Antanas
Siauciunas, Darius
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2019, 24 (01) : 20 - 33
[4] On Discrete Value Distribution of Certain Compositions
Garbaliauskiene, Virginija
Karaliunaite, Julija
Macaitiene, Renata
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2019, 24 (01) : 34 - 42
[5] THE RIEMANN HYPOTHESIS AND UNIVERSALITY OF THE RIEMANN ZETA-FUNCTION
Garunkstis, Ramunas
Laurincikas, Antanas
[J]. MATHEMATICA SLOVACA, 2018, 68 (04) : 741 - 748
[6] Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros
Garunkstis, Ramunas
Laurincikas, Antanas
[J]. PERIODICA MATHEMATICA HUNGARICA, 2018, 76 (02) : 217 - 228
[7] Zeros of the Riemann zeta-function and its universality
Garunkstis, Ramunas
Laurincikas, Antanas
Macaitiene, Renata
[J]. ACTA ARITHMETICA, 2017, 181 (02) : 127 - 142
[8] Universality of the periodic Hurwitz zeta-function
Javtokas, A.
Laurincikas, A.
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2006, 17 (10) : 711 - 722
[9] THE JOINT DISTRIBUTION OF PERIODIC ZETA-FUNCTIONS
Kacinskaite, Roma
Laurincikas, Antanas
[J]. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2011, 48 (02) : 257 - 279
[10] Kaczorowski J., 2009, New Directions in Value-Distribution Theory of Zeta and L-functions, Proceedings of the Wurzburg Conference, Wurzburg, Germany, 6-10 October 2008, P113

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