Möbius function is strongly orthogonal to polynomial phases over $\mathbb{F}_p[t]$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908722723291136 |
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| author | Milićević, Luka Ranđelović, Žarko |
| author_facet | Milićević, Luka Ranđelović, Žarko |
| contents | In this paper, we prove power-saving bounds for the corelation of the Möbius function with polynomial phases of degree $k$ in function fields $\mathbb{F}_p[t]$, when $p > k$. The proof relies on a new approximation result for phases of biased multilinear forms and the recently established strong bounds for the problem of finding bounded codimension varieties inside the dense ones. Along the way, we also obtain polynomial bounds in the inverse theorem for Gowers uniformity norms in the special case of polynomial phases in finite vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Möbius function is strongly orthogonal to polynomial phases over $\mathbb{F}_p[t]$ Milićević, Luka Ranđelović, Žarko Combinatorics Number Theory In this paper, we prove power-saving bounds for the corelation of the Möbius function with polynomial phases of degree $k$ in function fields $\mathbb{F}_p[t]$, when $p > k$. The proof relies on a new approximation result for phases of biased multilinear forms and the recently established strong bounds for the problem of finding bounded codimension varieties inside the dense ones. Along the way, we also obtain polynomial bounds in the inverse theorem for Gowers uniformity norms in the special case of polynomial phases in finite vector spaces. |
| title | Möbius function is strongly orthogonal to polynomial phases over $\mathbb{F}_p[t]$ |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2512.17633 |