On the density of rational lines on diagonal cubic hypersurfaces, II
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910270829363200 |
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| author | Parsell, Scott Yeon, Kiseok |
| author_facet | Parsell, Scott Yeon, Kiseok |
| contents | In this paper, we establish the expected asymptotic formula for the number of rational lines on a diagonal cubic hypersurface in 18 or more variables, improving on recent work of the second author. This is achieved via a refined mean value estimate for minor arcs that non-trivially exploits a shifting variables argument in both underlying dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30549 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the density of rational lines on diagonal cubic hypersurfaces, II Parsell, Scott Yeon, Kiseok Number Theory In this paper, we establish the expected asymptotic formula for the number of rational lines on a diagonal cubic hypersurface in 18 or more variables, improving on recent work of the second author. This is achieved via a refined mean value estimate for minor arcs that non-trivially exploits a shifting variables argument in both underlying dimensions. |
| title | On the density of rational lines on diagonal cubic hypersurfaces, II |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.30549 |