Distribution of the number of zeros of polynomials over a finite field
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913962804641792 |
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| author | Jain, Ritik Moon, Han-Bom Wu, Peter |
| author_facet | Jain, Ritik Moon, Han-Bom Wu, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14580 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Distribution of the number of zeros of polynomials over a finite field Jain, Ritik Moon, Han-Bom Wu, Peter Probability Combinatorics Number Theory 60C05, 11T06, 12E20, 05A1 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. |
| title | Distribution of the number of zeros of polynomials over a finite field |
| topic | Probability Combinatorics Number Theory 60C05, 11T06, 12E20, 05A1 |
| url | https://arxiv.org/abs/2308.14580 |