On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function

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Title: On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function
Authors: Mora, Gaspar | Sepulcre, Juan Matias
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Zeros of entire functions | Almost-periodic functions | Functional equations
Knowledge Area: Análisis Matemático
Date Created: 2008
Issue Date: 2-Oct-2008
Publisher: Elsevier
Citation: MORA MARTÍNEZ, Gaspar; SEPULCRE MARTÍNEZ, Juan Matías. “On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function”. Journal of Mathematical Analysis and Applications. Vol. 350, Issue 1 (1 Febr. 2009). ISSN 0022-247X, pp. 409-415
Abstract: In this paper we study the distribution of the zeros of each function G_{n}(z)≡1+2^{z}+...+n^{z}, n≥2, which approaches the Riemann zeta function for Rez<-1, and is closely related to the solutions of the functional equations f(z)+f(2z)+...+f(nz)=0. We determine the density of the zeros of G_{n}(z) on the critical strip where they are situated by using almost-periodic functions techniques. Furthermore, by using a theorem of Kronecker, we prove the existence in the critical strip of infinitely many rectangles for which we have found a formula to determine the number of zeros inside each rectangle with an error of ± 1 zero.
URI: http://hdl.handle.net/10045/13692
ISSN: 0022-247X (Print) | 1096-0813 (Online)
DOI: 10.1016/j.jmaa.2008.09.068
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.jmaa.2008.09.068
Appears in Collections:INV - CADAGL - Artículos de Revistas

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