ON SIMPLE ZEROS OF THE DEDEKIND ZETA-FUNCTION OF A QUADRATIC NUMBER FIELD

被引：2

作者：

Wu, Xiaosheng ^{[1
]}

Zhao, Lilu ^{[2
]}

机构：

[1] Hefei Univ Technol, Sch Math, Hefei 230009, Anhui, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

来源：

MATHEMATIKA | 2019年 / 65卷 / 04期

基金：

中国国家自然科学基金;

关键词：

11M06; 11M26; 11R42 (primary);

D O I：

10.1112/S0025579319000196

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the number of non-trivial simple zeros of the Dedekind zeta function of a quadratic number field in the rectangle {sigma +it : 0 < sigma < 1, 0 < t < T}. We prove that such a number exceeds T6/7-epsilon if T is sufficiently large. This improves upon the classical lower bound T-6/11 established by Conrey et al [Simple zeros of the zeta function of a quadratic number field. I. Invent. Math. 86 (1986), 563-576].

引用

页码：851 / 861

页数：11

共 50 条

[1] MEAN-VALUE THEOREM FOR THE DEDEKIND ZETA-FUNCTION OF A QUADRATIC NUMBER-FIELD
HINZ, JG
MONATSHEFTE FUR MATHEMATIK, 1979, 87 (03): : 229 - 239
[2] ON THE VALUES AT INTEGERS OF THE DEDEKIND ZETA-FUNCTION OF A REAL QUADRATIC FIELD
KRAMER, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 299 (01) : 59 - 79
[3] A NOTE ON MEAN VALUE OF DEDEKIND ZETA-FUNCTION OF QUADRATIC FIELD
MOTOHASHI, Y
MATHEMATISCHE ANNALEN, 1970, 188 (02) : 123 - +
[4] REAL ZEROS OF DEDEKIND ZETA FUNCTION OF AN IMAGINARY QUADRATIC FIELD
PURDY, GB
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (02): : A386 - A386
[5] SIMPLE ZEROS OF THE ZETA FUNCTION OF A QUADRATIC NUMBER-FIELD .1.
CONREY, JB
GHOSH, A
GONEK, SM
INVENTIONES MATHEMATICAE, 1986, 86 (03) : 563 - 576
[6] THE MEAN-SQUARE OF THE DEDEKIND ZETA-FUNCTION IN QUADRATIC NUMBER-FIELDS
MULLER, W
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1989, 106 : 403 - 417
[7] SIMPLE ZEROS OF THE RIEMANN ZETA-FUNCTION
ANDERSON, RJ
JOURNAL OF NUMBER THEORY, 1983, 17 (02) : 176 - 182
[8] On simple zeros of the Riemann zeta-function
Bui, H. M.
Heath-Brown, D. R.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2013, 45 : 953 - 961
[9] SIMPLE ZEROS OF THE RIEMANN ZETA-FUNCTION
CHEER, AY
GOLDSTON, DA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (02) : 365 - 372
[10] Simple zeros of the Riemann zeta-function
Conrey, JB
Ghosh, A
Gonek, SM
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1998, 76 : 497 - 522

← 1 2 3 4 5 →