3 papers
math.NT2026
On the Green-Tao theorem for sparse sets
Joni Teräväinen, Mengdi Wang
We establish the following quantitative form of the Green--Tao theorem: if a set of relative density within the primes up to contains no nontrivial arithmeti…
math.NT2024
Quantitative asymptotics for polynomial patterns in the primes
Lilian Matthiesen, Joni Teräväinen, Mengdi Wang
We prove quantitative estimates for averages of the von Mangoldt and Möbius functions along polynomial progressions for a large class of polynomials $P…
math.NT2024
Smooth numbers are orthogonal to nilsequences
Lilian Matthiesen, Mengdi Wang
The aim of this paper is to study distributional properties of integers without large or small prime factors. Define an integer to be -smooth if all of its prime factors be…