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

2024/09/10 by Ritik Jain, Jain, Ritik
Computer Science · #Algorithms and Data Compression #Chaos-based Image/Signal Encryption #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2409.06866

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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