An improved bound on the number of dot products determined by a finite point set in the plane
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916619334189056 |
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| author | Kokkinos, Michalis |
| author_facet | Kokkinos, Michalis |
| contents | We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the improved lower bound \[|\{p\cdot q : p,q\in P\}|\gtrsim |P|^{\frac2 3 + \frac{7}{1425}}.\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved bound on the number of dot products determined by a finite point set in the plane Kokkinos, Michalis Combinatorics Number Theory 52C10, 11B30 We are interested to bound from below the number of distinct dot products determined by a finite set of points $P$ in the Euclidean plane. In this paper, we build on the work of B. Hanson, O. Roche-Newton, and S. Senger, to obtain the improved lower bound \[|\{p\cdot q : p,q\in P\}|\gtrsim |P|^{\frac2 3 + \frac{7}{1425}}.\] |
| title | An improved bound on the number of dot products determined by a finite point set in the plane |
| topic | Combinatorics Number Theory 52C10, 11B30 |
| url | https://arxiv.org/abs/2502.12727 |