Abstract: There is a well-developed theory of uniform distribution of sequences of real numbers modulo 1 that tells us when a sequence equidistributes, in particular, we have explicit measures of "discrepancy" that tell us how fast such equidistribution occurs. For the p-adic numbers, the situation is, as usual, a bit more complicated in some regards. There are several notions of discrepancy in finite extensions of the p-adic numbers, but thus far, we have lacked a notion of discrepancy for sequences of complex p-adic numbers. We introduce such a notion, and prove that that sequences with discrepancy tending to zero equidistribute in the expected fashion for the p-adic unit disc. Our proof relies on a Berkovich unit disc analogue of the Weyl criterion. This is a preliminary report on joint work with Gwyn Hubbard.
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