p-进解析簇上的zeta函数

Zeta functions of p-adic analytic varieties

本文引进定义在p-进数域上p-进解析簇的zeta函数,该zeta函数计算解析簇上Techmuller点的个数.利用Witt向量的加法运算、Dwork有理性定理以及Hilbert基定理,本文证明该zeta函数是一个有理函数.本文还提出若干问题以促进对这类新的zeta函数的研究.

In this paper,we introduce the zeta function of a p-adic analytic variety de ned over a p-adic number eld.This zeta function counts Techmuller 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.