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Oct 30, 2021 at 22:48 comment added KConrad As Lubin has commented somewhere else on this site, it is a remarkable property that the well-behaved exponential (everywhere convergent, and homomorphism) and badly-behaved logarithm (finite radius of convergence, not a homomorphism) in complex analysis switch roles in $p$-adic analysis, where the logarithm is better behaved than the exponential in the sense of having a larger radius of convergence (although both are $p$-adically nice in being homomorphisms between their discs of convergence).
Oct 26, 2021 at 2:54 vote accept user474
Oct 23, 2021 at 18:16 history answered Lubin CC BY-SA 4.0