PreprintCC BY 4.0arXiv
On the density of rational lines on diagonal cubic hypersurfaces, II
Abstract
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.
Related
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BibTeX
@misc{parsell2026density,
title = {{On the density of rational lines on diagonal cubic hypersurfaces, II}},
author = {Scott Parsell and Kiseok Yeon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.30549},
eprint = {2605.30549},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30549},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the density of rational lines on diagonal cubic hypersurfaces, II
AU - Scott Parsell
AU - Kiseok Yeon
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2605.30549
UR - https://arxiv.org/abs/2605.30549
AB - 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.
ER -