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p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.
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votes
What is the value of $p$-adic $\zeta$-function at positive integer point?
Let me mention some irrationality results about p-adic zeta values:
In 2005, Frank Calegari arxiv link proved that for $p=2,3$, the p-adic zeta values $\zeta_p(3)$ is irrational (hence nonzero). It ca …