随机对称p-adic矩阵等价类的分布

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-06-19 DOI:10.1112/mtk.12212

Valeriya Kovaleva

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引用次数: 0

摘要

我们考虑具有根据Z p$\mathbb上的Haar测度分布的独立项的随机对称矩阵{Z}_p$，并推导出它们的正则形式关于几个等价关系的分布。我们给出了一些应用的例子，包括Bhargava、Cremona、Fisher、Jones和Keating关于Zp$\mathbb上的随机二次型的概率的结果的一个替代证明{Z}_p$有一个非平凡的零。

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On the distribution of equivalence classes of random symmetric p-adic matrices

We consider random symmetric matrices with independent entries distributed according to the Haar measure on $Z_{p}$ for odd primes p and derive the distribution of their canonical form with respect to several equivalence relations. We give a few examples of applications including an alternative proof for the result of Bhargava, Cremona, Fisher, Jones and Keating on the probability that a random quadratic form over $Z_{p}$ has a non-trivial zero.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.