Xuancheng Shao

most citedAdditive energies of subsets of discrete cubes

1 citations · 1 across the 3 of their papers we have counts for

collaborators

Showing math.NTShow all

2 papers · 1 filter

math.NT2024

Higher uniformity of arithmetic functions in short intervals II. Almost all intervals

Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2

We study higher uniformity properties of the von Mangoldt function $Λ$ , the Möbius function $μ$ , and the divisor functions $d_{k}$ on short intervals $(x, x + H]$ for almost all $x \in…

math.NT2024

Bounds in a popular multidimensional nonlinear Roth theorem

Sarah Peluse, Sean Prendiville, Xuancheng Shao

A nonlinear version of Roth's theorem states that dense sets of integers contain configurations of the form $x$ , $x + d$ , $x + d^{2}$ . We obtain a multidimensional version of this result…