4 citations · 8 across the 7 of their papers we have counts for
7 papers
On the density of rational lines on diagonal cubic hypersurfaces, II
Scott Parsell, Kiseok Yeon
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 t…
The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces
Julia Brandes, Scott T. Parsell
We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree and one general form of degree , where is smaller than . B…
On generating functions in additive number theory, II: Lower-order terms and applications to PDEs
Julia Brandes, Scott T. Parsell, Konstantinos Poulias +2
We obtain asymptotics for sums of the form involving lower order main terms. As an application, we show that for almost all one…
A Hardy-Ramanujan-Rademacher-type formula for -regular partitions
James Mc Laughlin, Scott Parsell
Let denote the number of partitions of a positive integer into parts containing no multiples of or , where and are square-free, relatively prime…
Simultaneous additive equations: Repeated and differing degrees
Julia Brandes, Scott T. Parsell
We obtain bounds for the number of variables required to establish Hasse principles, both for existence of solutions and for asymptotic formulae, for systems of additive equations…
Exceptional sets for Diophantine inequalities
Scott T. Parsell, Trevor D. Wooley
We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral…
Near-optimal mean value estimates for multidimensional Weyl sums
Scott T. Parsell, Sean M. Prendiville, Trevor D. Wooley
We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the…