A slight improvement on the Ball-Rivoal theorem
A slight improvement on the Ball-Rivoal theorem
We prove that the dimension of the $\mathbb{Q}$-linear span of $1,\zeta(3),\zeta(5),\ldots,\zeta(s-1)$ is at least $1.009 \cdot \log s/(1+\log 2)$ for any sufficiently large even integer $s$ and we claim that the constant $1.009$ can be improved further to $1.108$. This slightly refines a well-known result of Rivoal (2000) or Ball-Rivoal …