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Values of the Kubota-Leopoldt zeta function at integers
For a given prime $p$, the Kubota-Leopoldt zeta function $\zeta_p(s)$ is the unique continuous $p$-adic function on the $p$-adic integers $\mathbb{Z}_p$ that equals $(1-p^{-k})\zeta(k)$ at the negative integers $k$ of the form $k = 1 \mod (p-1)$ if $p>2$ and $k = 1 \mod 2$ if $p=2$. This table lists values of $\zeta_p(s)$ at certain integers $s$.
