a -超几何级数和Hasse-Witt矩阵的p进改进

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2021-08-09 DOI:10.1007/s12188-021-00243-1

Alan Adolphson, Steven Sperber

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引用次数: 4

摘要

我们将特征为p的有限域上的射影超曲面的ζ函数的p进单位根确定为某p进级数矩阵的特殊值之积的特征值。这个矩阵是一个乘积\(F(\varLambda ^p)^{-1}F(\varLambda )\)，其中在矩阵\(F(\varLambda )\)中的元素是a -超几何级数具有积分系数\(F(\varLambda )\)与p无关。

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A-hypergeometric series and a p-adic refinement of the Hasse-Witt matrix

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.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.