论文标题
关于蜂窝有理近似值$ζ（5）$
On cellular rational approximations to $ζ(5)$
论文作者
论文摘要
我们分析了某种蜂窝积分家族，它们是模量空间上的时期积分$ \ MATHCAL {M} _ {0,8} $零属曲线的$，带有八个标记点，这会导致同时理性的近似值至$ζ（3）$和$ζ（5）$。通过利用大型对称组对这些积分的作用，我们构建了许多有效的有效理性近似值$ p/q $至$ζ（5）$满足\ [0 <\ bigg |ζ（5） - \ frac pq \ big big big big | <\ frac1 {q^{q^{0.86}}}。 \]
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 $ζ(3)$ and $ζ(5)$. By exploiting the action of a large symmetry group on these integrals, we construct infinitely many effective rational approximations $p/q$ to $ζ(5)$ satisfying \[ 0<\bigg|ζ(5)-\frac pq\bigg|<\frac1{q^{0.86}}. \]
