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

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arxiv 2308.14580 v1 pith:QDRXIFDR submitted 2023-08-28 math.PR math.COmath.NT

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

classification math.PR math.COmath.NT
keywords distributionpolynomialsdegreefieldboundedfinitenumberprobability
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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.

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