| _version_ | 1866902093229457408 |
|---|---|
| author | TALLA WAFFO, Luc Ramses |
| author_facet | TALLA WAFFO, Luc Ramses |
| contents | <p>We investigate the values of the Riemann zeta function at odd integers <br>and the Dirichlet beta function at even integers, by collecting several distinct analytic <br>frameworks converging to these values, thus providing a unifying perspective. <br>Beyond analytic interest, these formulas motivate linear independence <br>conjectures which, if established, would imply the irrationality of the quantities<br>$\dfrac{\zeta(2n+1)}{\pi^{2n+1}}$ and $\dfrac{\beta(2n)}{\pi^{2n}}$.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17296067 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Perspectives on the arithmetic nature of the ratios $\dfrac{\zeta(2n+1)}{\pi^{2n+1}}$ and $\dfrac{\beta(2n)}{\pi^{2n}}$ TALLA WAFFO, Luc Ramses <p>We investigate the values of the Riemann zeta function at odd integers <br>and the Dirichlet beta function at even integers, by collecting several distinct analytic <br>frameworks converging to these values, thus providing a unifying perspective. <br>Beyond analytic interest, these formulas motivate linear independence <br>conjectures which, if established, would imply the irrationality of the quantities<br>$\dfrac{\zeta(2n+1)}{\pi^{2n+1}}$ and $\dfrac{\beta(2n)}{\pi^{2n}}$.</p> |
| title | Perspectives on the arithmetic nature of the ratios $\dfrac{\zeta(2n+1)}{\pi^{2n+1}}$ and $\dfrac{\beta(2n)}{\pi^{2n}}$ |
| url | https://doi.org/10.5281/zenodo.17296067 |