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arXiv · 2409.06866

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

Ritik Jain
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Abstract

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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Ritik Jain. 2024-09-10. The number of solutions of a random system of polynomials over a finite field. https://arxiv.org/abs/2409.06866

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