Bounding ζ (s) in the critical strip

被引：33

作者：

Carneiro, Emanuel ^{[1
]}

Chandee, Vorrapan ^{[2
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

JOURNAL OF NUMBER THEORY | 2011年 / 131卷 / 03期

基金：

美国国家科学基金会;

关键词：

Riemann zeta-function; Extremal functions; Exponential type;

D O I：

10.1016/j.jnt.2010.08.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming the Riemann Hypothesis, we make use of the recently discovered (Carneiro et al. (preprint) [1]) extremal majorants and minorants of prescribed exponential type for the function log(4+x(2)/(alpha-1/2)(2)+x(2)) to find upper and lower bounds with explicit constants for log vertical bar zeta(alpha + it)vertical bar in the critical strip, extending the work of Chandee and Soundararajan (in press) [4]. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：363 / 384

页数：22

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