Upper bounds for discrete moments of the derivatives of the riemann zeta-function on the critical line*

被引：4

作者：

Christ, Thomas ^{[1
]}

Kalpokas, Justas ^{[2
]}

机构：

[1] Univ Wurzburg, Dept Math, Emil Fischer Str 40, D-97074 Wurzburg, Germany

[2] Vilnius State Univ, Fac Math & Informat, LT-03225 Vilnius, Lithuania

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2012年 / 52卷 / 03期

关键词：

Riemann zeta-function; value-distribution; critical line; FRACTIONAL MOMENTS;

D O I：

10.1007/s10986-012-9170-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming the Riemann hypothesis, we establish upper bounds for discrete moments of the Riemann zeta-function and its derivatives on the critical line. Moreover, we express continuous moments of the Riemann zeta-function and its derivatives in terms of these discrete moments. This allows us to give conditional upper bounds for , where l and k are nonnegative integers.

引用

页码：233 / 248

页数：16

共 26 条

[1]

Bogachev V. I., 2007, MEASURE THEORY, V2, DOI DOI 10.1007/978-3-540-34514-5

[2]

Bogachev VI., 2007, MEASURE THEORY, VI, II

[3]

Christ T., LOWER BOUNDS D UNPUB

[4] SIZE OF RIEMANN ZETA-FUNCTION AT PLACES SYMMETRIC WITH RESPECT TO POINT 1/2 [J].

DIXON, RD ;

SCHOENFE.L .

DUKE MATHEMATICAL JOURNAL, 1966, 33 (02) :291-&

[5]

Edwards H.M., 1974, Riemann's Zeta Function

[6]

Gonek S.M., 1985, TOPICS ANAL NUMBER T

[7]

Gonek S. M., 1993, CONT MATH, V143, P395

[8] MEAN-VALUES OF THE RIEMANN ZETA-FUNCTION AND ITS DERIVATIVES [J].

GONEK, SM .

INVENTIONES MATHEMATICAE, 1984, 75 (01) :123-141

[9] Note about zeros in the zeta(s) function of Reimann [J].

Gram, JP .

ACTA MATHEMATICA, 1903, 27 (01) :289-304

[10]

HARDY GH, 1936, P ROYAL SOC A, V113, P542

← 1 2 3 →