Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros

被引：6

作者：

Garunkstis, Ramunas ^{[1
]}

Laurincikas, Antanas ^{[1
]}

机构：

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

来源：

PERIODICA MATHEMATICA HUNGARICA | 2018年 / 76卷 / 02期

关键词：

Riemann zeta-function; Riemann hypothesis; Discrete mean square; THEOREM; LANDAU;

D O I：

10.1007/s10998-017-0228-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Assume the Riemann hypothesis. On the right-hand side of the critical strip, we obtain an asymptotic formula for the discrete mean square of the Riemann zeta-function over imaginary parts of its zeros.

引用

页码：217 / 228

页数：12

共 50 条

[31] Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta-Function
SamirH Saker
Journal of Inequalities and Applications, 2010
[32] ON ZEROS OF SOME ANALYTIC FUNCTIONS RELATED TO THE RIEMANN ZETA-FUNCTION
Laurincikas, Antanas
GLASNIK MATEMATICKI, 2013, 48 (01) : 59 - 65
[33] On the mean square of the zeta-function and the divisor problem
Ivic, Aleksandar
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2007, 32 (01) : 269 - 277
[34] DISCRETE UNIVERSALITY OF THE RIEMANN ZETA-FUNCTION IN SHORT INTERVALS
Laurincikas, Antanas
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2020, 14 (02) : 382 - 405
[35] THE RIEMANN HYPOTHESIS AND UNIVERSALITY OF THE RIEMANN ZETA-FUNCTION
Garunkstis, Ramunas
Laurincikas, Antanas
MATHEMATICA SLOVACA, 2018, 68 (04) : 741 - 748
[36] On the Discrete Approximation by the Mellin Transform of the Riemann Zeta-Function
Garbaliauskiene, Virginija
Laurincikas, Antanas
Siauciunas, Darius
MATHEMATICS, 2023, 11 (10)
[37] The prime number theorem and pair correlation of zeros of the Riemann zeta-function
D. A. Goldston
Ade Irma Suriajaya
Research in Number Theory, 2022, 8
[38] The Mellin transform of the square of the Riemann zeta-function in the critical strip
Laurincikas, A.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2011, 22 (07) : 467 - 476
[39] On simple zeros of the Riemann zeta-function in short intervals on the critical line
Steuding, J
ACTA MATHEMATICA HUNGARICA, 2002, 96 (04) : 259 - 308
[40] Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function
Renata Macaitienė
Darius Šiaučiūnas
Lithuanian Mathematical Journal, 2019, 59 : 81 - 95

← 1 2 3 4 5 →