有限域上随机多项式系统的解数

arXiv - MATH - Probability Pub Date : 2024-09-10 DOI:arxiv-2409.06866

Ritik Jain

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引用次数: 0

摘要

我们研究有限交换环 R$ 上 $m$ 随机 $n$ 变量多项式系统的公共零点数的概率分布。我们计算 R$ 上多项式系统的期望公共零点数。然后，在 $R$ 是一个域的情况下，根据样本空间的必要和充分条件，我们证明公有零点数是二项式分布的。

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The number of solutions of a random system of polynomials over a finite field

We study the probability distribution of the number of common zeros of a system of $m$ random $n$-variate polynomials over a finite commutative ring $R$. We compute the expected number of common zeros of a system of polynomials over $R$. Then, in the case that $R$ is a field, under a necessary-and-sufficient condition on the sample space, we show that the number of common zeros is binomially distributed.

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arXiv - MATH - Probability

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