Counting (skew-)reciprocal Littlewood polynomials with square discriminant
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916785926701056 |
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| author | Hokken, David |
| author_facet | Hokken, David |
| contents | A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant. This relates to a bounded-height analogue of the Van der Waerden conjecture on Galois groups of random polynomials. As a byproduct, we establish the asymptotics of certain Gaussian-weighted counts of Pythagorean triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Counting (skew-)reciprocal Littlewood polynomials with square discriminant Hokken, David Number Theory Combinatorics Primary: 11C08, 11R32, 11R09, 05A16. Secondary: 11P21 A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant. This relates to a bounded-height analogue of the Van der Waerden conjecture on Galois groups of random polynomials. As a byproduct, we establish the asymptotics of certain Gaussian-weighted counts of Pythagorean triples. |
| title | Counting (skew-)reciprocal Littlewood polynomials with square discriminant |
| topic | Number Theory Combinatorics Primary: 11C08, 11R32, 11R09, 05A16. Secondary: 11P21 |
| url | https://arxiv.org/abs/2301.05656 |