GAPS BETWEEN ZEROS OF THE RIEMANN ZETA-FUNCTION

被引：11

作者：

Bui, H. M. ^{[1
]}

Milinovich, M. B. ^{[2
]}

机构：

[1] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2018年 / 69卷 / 02期

关键词：

CONSECUTIVE ZEROS; CRITICAL LINE;

D O I：

10.1093/qmath/hax047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than 3.18 times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the Riemann zeta-function on the critical line (if such zeros exist).

引用

页码：403 / 423

页数：21

共 50 条

[31] On Lerch's formula and zeros of the quadrilateral zeta function
Nakamura, Takashi
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2025,
[32] Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
Dixit, Atul
Robles, Nicolas
Roy, Arindam
Zaharescu, Alexandru
JOURNAL OF NUMBER THEORY, 2015, 149 : 404 - 434
[33] On Titchmarsh’s Phenomenon in the Theory of the Riemann Zeta Function
S. V. Konyagin
M. A. Korolev
Proceedings of the Steklov Institute of Mathematics, 2022, 319 : 169 - 188
[34] Small values of the Riemann zeta function on the critical line
Kalpokas, Justas
Sarka, Paulius
ACTA ARITHMETICA, 2015, 169 (03) : 201 - 220
[35] On Titchmarsh's Phenomenon in the Theory of the Riemann Zeta Function
Konyagin, S. V.
Korolev, M. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2022, 319 (01) : 169 - 188
[36] GRAM'S LAW AND THE ARGUMENT OF THE RIEMANN ZETA FUNCTION
Korolev, Maxim
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2012, 92 (106): : 53 - 78
[37] On Repeated Values of the Riemann Zeta Function on the Critical Line
Banks, William D.
Kang, Sarah
EXPERIMENTAL MATHEMATICS, 2012, 21 (02) : 132 - 140
[38] More than 41% of the zeros of the zeta function are on the critical line
Bui, H. M.
Conrey, Brian
Young, Matthew P.
ACTA ARITHMETICA, 2011, 150 (01) : 35 - 64
[39] Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts
Dixit, Atul
Kumar, Rahul
Maji, Bibekananda
Zaharescu, Alexandru
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 466 (01) : 307 - 323
[40] Self-intersections of the Riemann zeta function on the critical line
Banks, William
Castillo-Garate, Victor
Fontana, Luigi
Morpurgo, Carlo
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 406 (02) : 475 - 481

← 1 2 3 4 5 →