次多项式n$n$ / Zp${\mathbb {Z}}_p$在Qp${\mathbb {Q}}_p$中恰好有r$r$根的密度

IF 1.5 1区数学 Q1 MATHEMATICS

Proceedings of the London Mathematical Society Pub Date : 2022-03-17 DOI:10.1112/plms.12438

M. Bhargava, J. Cremona, T. Fisher, Stevan Gajović

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引用次数: 2

摘要

我们确定了在Zp$｛\mathbb｛Z｝｝_p$上的n$n$次随机多项式在Qp${\mathbb{Q｝}_p$中恰好有r$r$根的概率，并证明了它是由p$p$的有理函数给出的，该有理函数在用1/p$1/p$替换p$p$时是不变的。

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The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$

We determine the probability that a random polynomial of degree n$n$ over Zp${\mathbb {Z}}_p$ has exactly r$r$ roots in Qp${\mathbb {Q}}_p$ , and show that it is given by a rational function of p$p$ that is invariant under replacing p$p$ by 1/p$1/p$ .

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来源期刊

Proceedings of the London Mathematical Society 数学-数学

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Proceedings of the London Mathematical Society is the flagship journal of the LMS. It publishes articles of the highest quality and significance across a broad range of mathematics. There are no page length restrictions for submitted papers. The Proceedings has its own Editorial Board separate from that of the Journal, Bulletin and Transactions of the LMS.