An estimate of the lower bound of the real parts of the zeros of the partial sums of the Riemann zeta function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Mora, G.

关键词: Zeros of the partial sums of the Ricinarm zeta function;   

DOI  :  10.1016/j.jmaa.2015.02.028

来源: Elsevier

【 摘 要 】

Let zeta(n) (z) := Sigma(n)(kn=1) 1/k(z), z = x + iy, be the nth partial sum of the Riemann zeta function and a(zeta n(z)) := inf {Rz : zeta(n)(z) = 0}. In this paper we prove that a(zeta n(z)) = -log 2/log(n-1/n-2) + Delta(n), n > 2, with lim sup(n -> x) vertical bar Delta(n)vertical bar <= log 2. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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