6 papers
Linnik's problem for multiplicative functions
Kaisa Matomäki, Joni Teräväinen
We study a multiplicative function analogue of Linnik's problem on the least prime in an arithmetic progression. Let be a multiplica…
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
Tim Browning, Efthymios Sofos, Joni Teräväinen
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish…
Bounds on the exceptional set in the conjecture
Christian Bernert, Tim Browning, Jared Duker Lichtman +1
We study solutions to the equation , where form a triple of coprime natural numbers. The conjecture asserts that, for any , such triples satisfy $\mathrm…
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 infi…
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…
Higher uniformity of arithmetic functions in short intervals II. Almost all intervals
Kaisa Matomäki, Maksym RadziwiÅÅ, 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 \…