| Título: | On the distribution of zeros of a sequence of entire functions approaching the Riemann zeta function |
| Autores: |
Mora Martínez, Gaspar Sepulcre Martínez, Juan Matías |
| Fecha: |
2010-03-24 2010-03-24 2008 2008-10-02 |
| Publicador: | RUA Docencia |
| Fuente: |
 |
| Tipo: | info:eu-repo/semantics/article |
| Tema: |
Zeros of entire functions Almost-periodic functions Functional equations Análisis Matemático |
| Descripción: | 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. |
| Idioma: | Inglés |
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