An Unexpected Connection Between the Discrete Zeta Function and the Erdos-Straus Conjecture Under Mballa's Conjecture
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918019152740352 |
|---|---|
| author | Mballa, Philemon Urbain |
| author_facet | Mballa, Philemon Urbain |
| contents | In this article, we establish an additive decomposition of the discrete zeta function (for $s \in \mathbb{N}^*$, $s > 1$), more precisely of the function $4(ζ(s)-1)$, as a series whose general term is of the form $1/x_n(s) + 1/y_n(s) + 1/z_n(s)$, where $x_n(s), y_n(s), z_n(s)$ are solutions of the Erdos--Straus conjecture under a personal conjecture (which I will refer to here as Mballa's Conjecture) that I formulated by parametrization in the article: arXiv:2502.20935. This connection thus builds a bridge between analysis and Egyptian fractions in general, and the Erdos--Straus conjecture in particular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Unexpected Connection Between the Discrete Zeta Function and the Erdos-Straus Conjecture Under Mballa's Conjecture Mballa, Philemon Urbain Number Theory In this article, we establish an additive decomposition of the discrete zeta function (for $s \in \mathbb{N}^*$, $s > 1$), more precisely of the function $4(ζ(s)-1)$, as a series whose general term is of the form $1/x_n(s) + 1/y_n(s) + 1/z_n(s)$, where $x_n(s), y_n(s), z_n(s)$ are solutions of the Erdos--Straus conjecture under a personal conjecture (which I will refer to here as Mballa's Conjecture) that I formulated by parametrization in the article: arXiv:2502.20935. This connection thus builds a bridge between analysis and Egyptian fractions in general, and the Erdos--Straus conjecture in particular. |
| title | An Unexpected Connection Between the Discrete Zeta Function and the Erdos-Straus Conjecture Under Mballa's Conjecture |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.08716 |