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Distribution of
the number of zeros of polynomials over a finite field
Ritik Jain, Han-Bom Moon and Peter Wu |
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Vol. 18 (2025), No. 4, 707–718
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Abstract |
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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 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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Keywords
finite field, probability distribution, number of roots
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Mathematical Subject Classification
Primary: 05A15, 11T06, 60C05
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Milestones
Received: 21 September 2023
Revised: 12 April 2024
Accepted: 19 April 2024
Published: 30 July 2025
Communicated by Anant Godbole
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Authors |
| Ritik Jain | |
| Department of Mathematics Fordham University New York, NY United States |
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| Han-Bom Moon | |
| Department of Mathematics Fordham University New York, NY United States |
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| Peter Wu | |
| Department of Mathematics Fordham University New York, NY United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
