Xuancheng Shao

collaborators

4 papers

math.CO2025

On exponential Freiman dimension

Jeck Lim, Akshat Mudgal, Cosmin Pohoata +1

The exponential Freiman dimension of a finite set $A \subset R^{m}$ , introduced by Green and Tao in 2006, represents the largest positive integer $d$ for which $A$ contain…

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…

math.CO2024

Additive energies of subsets of discrete cubes

Xuancheng Shao

For a positive integer $n \geq 2$ , define $t_{n}$ to be the smallest number such that the additive energy $E (A)$ of any subset $A \subset {0, 1, \dots, n - 1}^{d}$ and any $d$ is at most…