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

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Title: An estimate of the lower bound of the real parts of the zeros of the partial sums of the Riemann zeta function
Authors: Mora, Gaspar
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Zeros of the partial sums of the Riemann zeta function
Knowledge Area: Análisis Matemático
Issue Date: 1-Jul-2015
Publisher: Elsevier
Citation: Journal of Mathematical Analysis and Applications. 2015, 427(1): 428-439. doi:10.1016/j.jmaa.2015.02.028
Abstract: Let View the MathML source ζn(z):=∑k=1n1kz, z=x+iy, be the n th partial sum of the Riemann zeta function and aζn(z):=inf⁡{ℜz:ζn(z)=0}. In this paper we prove that View the MathML source aζn(z)=−log⁡2log⁡(n−1n−2)+Δn, n>2, with lim⁡supn→∞ |Δn|≤log⁡2.
URI: http://hdl.handle.net/10045/45956
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2015.02.028
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2015 Elsevier Inc.
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2015.02.028
Appears in Collections:INV - CADAGL - Artículos de Revistas

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