arXiv:2308.14580 Abstract | arXiv Analytics

arXiv:2308.14580 [math.PR]Abstract References Reviews Resources

Distribution of the number of zeros of polynomials over a finite field

Published 2023-08-28Version 1

We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the single variable case, we show that as the degree of the polynomials and the order of the field simultaneously approach infinity, the distribution converges to a Poisson distribution.

Comments: 12 pages, an REU project at Fordham University

Categories: math.PR, math.CO, math.NT

Subjects: 60C05, 11T06, 12E20

Keywords: finite field, field simultaneously approach infinity, poisson distribution, distribution converges, probability generating function

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