IGUSA LOCAL ZETA FUNCTION OF THE POLYNOMIAL $f(x)=x_{1}^{m}+x_{2}^{m}+¥cdots+x_{n}^{m}$
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概要
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We determine an explicit formula for the Igusa local zeta function corresponding to the character $¥chi=1$ and the polynomial $f(x)=x_{1}^{m}+x_{2}^{m}+$ . . $.+x_{n}^{m}$ over the p-adic field $¥mathbb{Q}_{p}$ , for an arbitrary rational prime $p$ and a positive rational integer $m$ satisfying gcd $(m,p)=gcd(m,p-1)=1$ .
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