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arxiv: 2605.30549 · v1 · pith:MVS3GW36new · submitted 2026-05-28 · 🧮 math.NT

On the density of rational lines on diagonal cubic hypersurfaces, II

classification 🧮 math.NT
keywords cubicdiagonallinesrationalvariablesachievedarcsargument
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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.

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