Q-binomials and non-continuity of the p-adic Fourier transform
Abstract
Let F be a finite extension of Qp. We show that every Schwartz function on F, with values in an algebraic closure of Qp, is the uniform limit of a sequence of Schwartz functions, whose Fourier transforms tend uniformly to 0. The proof uses the notion of q-binomial coefficients and some classical identities between them.
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