Uniform p-adic cell decomposition and local zeta functions
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چکیده
The purpose of this paper is to give a cell decomposition for p-adic fields, uniform in p. This generalizes a cell decomposition for fixed p, proved by Denef [7], [9]. We also give some applications of our cell decomposition. A first implication is a uniform quantifier elimination for p-adic fields. Beiair [2], Delon [6] and Weispfenning [16] obtained quantifier elimination in other languages, but the language we use seems more practical for the evaluation of p-adic integrals. As a second application, we reprove results of Denef [10] on the dependence on p of the Igusa local zeta function. In this context we also obtain new results on p-adic integrals over sets definable in a language with cross section.
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