X. Shao

activity

20072022

most citedType-II/III DCT/DST algorithms with reduced number of arithmetic operations

60 citations · 281 across the 30 of their papers we have counts for

collaborators

Showing 2016Show all

4 papers · 1 filter

math.NT2016★ 27 cited

Vinogradov's theorem with almost equal summands

Kaisa Matomäki, James Maynard, Xuancheng Shao

Let $θ > 11/20$ . We prove that every sufficiently large odd integer $n$ can be written as a sum of three primes $n = p_{1} + p_{2} + p_{3}$ with $∣ p_{i} - n /3∣ \leq n^{θ}$ for $i \in {1, 2, 3}$ …

math.NT2016★ 3 cited

Gowers norms of multiplicative functions in progressions on average

Xuancheng Shao

Let $μ$ be the Möbius function and let $k \geq 1$ . We prove that the Gowers $U^{k}$ -norm of $μ$ restricted to progressions ${n \leq X : n \equiv a_{q} (mod q)}$ is $o (1)$ on average ov…

math.PR2016★ 17 cited

Upper tails for arithmetic progressions in a random set

Bhaswar B. Bhattacharya, Shirshendu Ganguly, Xuancheng Shao +1

Let $X_{k}$ denote the number of $k$ -term arithmetic progressions in a random subset of $Z / N Z$ or ${1, \dots, N}$ where every element is included independently wi…

math.NT2016★ 4 cited

Weyl sums, mean value estimates, and Waring's problem with friable numbers

Sary Drappeau, Xuancheng Shao

In this paper we study Weyl sums over friable integers (more precisely $y$ -friable integers up to $x$ when $y = (lo g x)^{C}$ for a large constant $C$ ). In particular, we obtain an a…