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

[1] On gaps between zeros of the Riemann zeta-function
Feng, Shaoji
Wu, Xiaosheng
[J]. JOURNAL OF NUMBER THEORY, 2012, 132 (07) : 1385 - 1397
[2] On the distribution of gaps between zeros of the Riemann zeta-function
Soundararajan, K
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1996, 47 (187): : 383 - 387
[3] ON THE GAPS BETWEEN THE CONSECUTIVE ZEROS OF THE RIEMANN ZETA-FUNCTION
FUJII, A
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1990, 66 (04) : 97 - 100
[4] A NOTE ON THE DISTRIBUTION OF GAPS BETWEEN ZEROS OF THE RIEMANN ZETA-FUNCTION
Wu, Xiaosheng
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (03) : 851 - 857
[5] On r-gaps between zeros of the Riemann zeta-function
Conrey, J. Brian
Turnage-Butterbaugh, Caroline L.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (02) : 349 - 356
[6] A NOTE ON THE GAPS BETWEEN CONSECUTIVE ZEROS OF THE RIEMANN ZETA-FUNCTION
Bui, H. M.
Milinovich, M. B.
Ng, N. C.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (12) : 4167 - 4175
[7] Large gaps between consecutive zeros of the Riemann zeta-function
Bui, H. M.
[J]. JOURNAL OF NUMBER THEORY, 2011, 131 (01) : 67 - 95
[8] A note on r-gaps between zeros of the Riemann zeta-function
Inoue, Shota
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2024, 56 (07) : 2268 - 2277
[9] GAPS BETWEEN CONSECUTIVE ZEROS OF THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE
IVIC, A
JUTILA, M
[J]. MONATSHEFTE FUR MATHEMATIK, 1988, 105 (01): : 59 - 73
[10] A small improvement in the gaps between consecutive zeros of the Riemann zeta-function
Preobrazhenskiĭ S.
[J]. Research in Number Theory, 2 (1)

← 1 2 3 4 5 →