Orthogonality of the Möbius function to polynomials with applications to Linear Equations in Primes over $\mathbb{F}_p[x]$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909347142959104 |
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| author | Meilin, Tal |
| author_facet | Meilin, Tal |
| contents | We prove that the Möbius function is orthogonal to polynomials over $\mathbb{F}_q[x]$ (up to a characteristic condition). We use this orthogonality property to count prime solutions to affine-linear equations of bounded complexity in $\mathbb{F}_p[x]$, with analog to a work of Green and Tao. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthogonality of the Möbius function to polynomials with applications to Linear Equations in Primes over $\mathbb{F}_p[x]$ Meilin, Tal Number Theory We prove that the Möbius function is orthogonal to polynomials over $\mathbb{F}_q[x]$ (up to a characteristic condition). We use this orthogonality property to count prime solutions to affine-linear equations of bounded complexity in $\mathbb{F}_p[x]$, with analog to a work of Green and Tao. |
| title | Orthogonality of the Möbius function to polynomials with applications to Linear Equations in Primes over $\mathbb{F}_p[x]$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.02480 |