We identify the p-adic unit roots of the zeta function of a projective hypersurface over a finite field of characteristic p as the eigenvalues of a product of special values of a certain matrix of p-adic series. That matrix is a product \(F(\varLambda ^p)^{-1}F(\varLambda )\), where the entries in the matrix \(F(\varLambda )\) are A-hypergeometric series with integral coefficients and \(F(\varLambda )\) is independent of p.

中文翻译：

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A-超几何级数和 Hasse-Witt 矩阵的 p-adic 细化

我们将特征p的有限域上的射影超曲面的 zeta 函数的p- adic 单位根识别为p- adic 系列的某个矩阵的特殊值的乘积的特征值。该矩阵是乘积\(F(\varLambda ^p)^{-1}F(\varLambda )\)，其中矩阵\(F(\varLambda )\)中的条目是具有积分系数的超几何级数和\(F(\varLambda )\)独立于 p。