19 citations · 20 across the 5 of their papers we have counts for
12 papers
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_…
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…
Frobenian multiplicative functions and rational points in fibrations
Daniel Loughran, Lilian Matthiesen
We consider the problem of counting the number of varieties in a family over with a rational point. We obtain lower bounds for this counting problem for some families…
Linear correlations of multiplicative functions
Lilian Matthiesen
We prove a Green--Tao theorem for multiplicative functions.
A consequence of the factorisation theorem for polynomial orbits on nilmanifolds
Lilian Matthiesen
We discuss a consequence of Green and Tao's factorisation theorem for polynomial orbits on nilmanifolds, adjusted to the requirements of certain arithmetic applications. More preci…
On the square-free representation function of a norm form and nilsequences
Lilian Matthiesen
We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previ…