In this paper,we introduce the zeta function of a p-adic analytic variety defined over a p-adic number field.This zeta function counts Techmüller points on the analytic variety.We prove that this zeta function is a rational function.Our approach is based on the addition operation of Witt vectors,Dwork's rationality theorem,and Hilbert's basis theorem.We also propose some problems to prompt the research on this new kind of zeta function.
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