In this short communication, we first report a closed-form formula for calculating the $\alpha$-divergences and the Sharma-Mittal divergences between any two zeta distributions. Then we report a formula to calculate the Kullback-Leibler divergence between any two zeta distributions. We illustrate these formula with examples.

翻译：在这个简短的通信中,我们第一次报告一个用于计算 $\ alpha$- divegences 和 Sharma-Mittal 任何两个 zeta 分布差异的封闭式公式。 然后我们报告一个计算 Kullback- Leibler 两种 zeta 分布差异的公式。 我们用示例来说明这些公式 。