arXiv subjects

Scott Parsell

Publications and source records attributed to Scott Parsell.

2 recordsLinked to original sources

arXiv2026

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

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.

math.NT↗

arXiv2019

A Hardy-Ramanujan-Rademacher-type formula for $(r,s)$-regular partitions

Let $p_{r,s}(n)$ denote the number of partitions of a positive integer $n$ into parts containing no multiples of $r$ or $s$, where $r>1$ and $s>1$ are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type infinite series for $p_{r,s}(n)$.

math.NT↗