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 arithmetic…
math.NT2025
Quantitative correlations and some problems on prime factors of consecutive integers
Terence Tao, Joni Teräväinen
We consider several old problems involving the number of prime divisors function , as well as the related functions and . Firstly, we show that there are infinit…
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 , the Möbius function , and the divisor functions on short intervals for almost all $x \in…