On cellular rational approximations to $\zeta(5)$
| Autor: | Brown, Francis, Zudilin, Wadim |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We analyse a certain family of cellular integrals, which are period integrals on the moduli space $\mathcal{M}_{0,8}$ of curves of genus zero with eight marked points, which give rise to simultaneous rational approximations to $\zeta(3)$ and $\zeta(5)$. By exploiting the action of a large symmetry group on these integrals, we construct infinitely many effective rational approximations $p/q$ to $\zeta(5)$ satisfying \[ 0<\bigg|\zeta(5)-\frac pq\bigg|<\frac1{q^{0.86}}. \] Comment: 31 pages, 2 figures |
| Databáze: | arXiv |
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