Algebraic representatives of the ratios $ζ(2n+1)/π^{2n}$ and $β(2n)/π^{2n-1}$
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910134107635712 |
|---|---|
| author | Waffo, Luc Ramsès Talla |
| author_facet | Waffo, Luc Ramsès Talla |
| contents | In \cite{TallaWaffo2025arxiv2511.02843} we introduced even polynomials $Ξ_n,Λ_n\in\mathbb{Q}[x]$ arising from integral representations of $β(2n)/π^{2n-1}$ and $ζ(2n+1)/π^{2n}$. In this paper we give explicit closed formulae for these polynomials in terms of Eulerian numbers and study their structural properties. These properties may prove useful in studies on the arithmetic nature of the ratios $β(2n)/π^{2n}$ and $ζ(2n+1)/π^{2n+1}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebraic representatives of the ratios $ζ(2n+1)/π^{2n}$ and $β(2n)/π^{2n-1}$ Waffo, Luc Ramsès Talla Number Theory In \cite{TallaWaffo2025arxiv2511.02843} we introduced even polynomials $Ξ_n,Λ_n\in\mathbb{Q}[x]$ arising from integral representations of $β(2n)/π^{2n-1}$ and $ζ(2n+1)/π^{2n}$. In this paper we give explicit closed formulae for these polynomials in terms of Eulerian numbers and study their structural properties. These properties may prove useful in studies on the arithmetic nature of the ratios $β(2n)/π^{2n}$ and $ζ(2n+1)/π^{2n+1}.$ |
| title | Algebraic representatives of the ratios $ζ(2n+1)/π^{2n}$ and $β(2n)/π^{2n-1}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.16761 |