Smooth polynomials with several prescribed coefficients
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911703690641408 |
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| author | Mérai, László |
| author_facet | Mérai, László |
| contents | Let $\mathbb{F}_q[t]$ be the polynomial ring over the finite field $\mathbb{F}_q$ of $q$ elements. A polynomial in $\mathbb{F}_q[t]$ is called $m$-smooth (or $m$-friable) if all its irreducible factors are of degree at most $m$. In this paper, we investigate the distribution of $m$-smooth (or $m$-friable) polynomials with prescribed coefficients. Our technique is based on character sum estimates on smooth (friable) polynomials, Bourgains's argument (2015) applied for polynomials by Ha (2016) and on double character sums on smooth (friable) polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smooth polynomials with several prescribed coefficients Mérai, László Number Theory Let $\mathbb{F}_q[t]$ be the polynomial ring over the finite field $\mathbb{F}_q$ of $q$ elements. A polynomial in $\mathbb{F}_q[t]$ is called $m$-smooth (or $m$-friable) if all its irreducible factors are of degree at most $m$. In this paper, we investigate the distribution of $m$-smooth (or $m$-friable) polynomials with prescribed coefficients. Our technique is based on character sum estimates on smooth (friable) polynomials, Bourgains's argument (2015) applied for polynomials by Ha (2016) and on double character sums on smooth (friable) polynomials. |
| title | Smooth polynomials with several prescribed coefficients |
| topic | Number Theory |
| url | https://arxiv.org/abs/2307.10280 |