Bounding ζ (s) in the critical strip

JOURNAL OF NUMBER THEORY

卷:131

Article

Carneiro, Emanuel¹  Chandee, Vorrapan² 

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

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

关键词: Riemann zeta-function;    Extremal functions;    Exponential type;   

DOI  :  10.1016/j.jnt.2010.08.002

来源: Elsevier

【 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.

【 授权许可】

Free