On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Bui, H. M.¹  Lester, S. J.²  Milinovich, M. B.³ 

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[2] Univ Rochester, Dept Math, Rochester, NY 14627 USA

[3] Univ Mississippi, Dept Math, University, MS 38677 USA

关键词: Riemann zeta-function;    Riemann Hypothesis;    Resonance method;    Omega theorems;   

DOI  :  10.1016/j.jmaa.2013.06.063

来源: Elsevier

【 摘 要 】

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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