Sphere intersections and incidences over finite fields
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915524716265472 |
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| author | Koh, Doowon Lund, Ben Xu, Chuandong Yoo, Semin |
| author_facet | Koh, Doowon Lund, Ben Xu, Chuandong Yoo, Semin |
| contents | We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the number of spheres is not too large. Our approach also leads to an elementary proof of the Iosevich-Rudnev bound on the Erdős-Falconer distance problem in odd dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sphere intersections and incidences over finite fields Koh, Doowon Lund, Ben Xu, Chuandong Yoo, Semin Combinatorics We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the number of spheres is not too large. Our approach also leads to an elementary proof of the Iosevich-Rudnev bound on the Erdős-Falconer distance problem in odd dimensions. |
| title | Sphere intersections and incidences over finite fields |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2509.25997 |