132 citations · 277 across the 17 of their papers we have counts for
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Vinogradov's three primes theorem with almost twin primes
Kaisa Matomäki, Xuancheng Shao
In this paper we prove two results concerning Vinogradov's three primes theorem with primes that can be called almost twin primes. First, for any , every sufficiently large odd…
Sign patterns of the Liouville and Möbius functions
Kaisa Matomäki, Maksym Radziwiłł, Terence Tao
Let and denote the Liouville and Möbius functions respectively. Hildebrand showed that all eight possible sign patterns for occur infinitely often.…
When the sieve works II
Kaisa Matomäki, Xuancheng Shao
For a set of primes , let be the number of positive integers all of whose prime factors lie in . In this paper we classify…
An averaged form of Chowla's conjecture
Kaisa Matomäki, Maksym Radziwiłł, Terence Tao
Let denote the Liouville function. A well known conjecture of Chowla asserts that for any distinct natural numbers , one has $\sum_{1 \leq n \leq X} λ(n+h_1) \do…
Multiplicative functions in short intervals
Kaisa Matomäki, Maksym Radziwiłł
We introduce a general result relating "short averages" of a multiplicative function to "long averages" which are well understood. This result has several consequences. First, for…
Small scale distribution of zeros and mass of modular forms
Stephen Lester, Kaisa Matomäki, Maksym Radziwiłł
We study the behavior of zeros and mass of holomorphic Hecke cusp forms on at small scales. In particular, we examine the distribution of the…