On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10045/13692
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 INV - GAM - Artículos de Revistas |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Distribution of zeros of Gn(z).tex | Preprint (acceso libre) | 26,08 kB | TeX | Open |
Distribution_of_zeros_of_Gn(z).pdf | Versión final (acceso restringido) | 162,47 kB | Adobe PDF | Open Request a copy |
Items in RUA are protected by copyright, with all rights reserved, unless otherwise indicated.