Kaisa Matomäki

An averaged form of Chowla’s conjecture

Let

On signs of Fourier coefficients of cusp forms

\lambda

DIOPHANTINE APPROXIMATION BY PRIMES

denote the Liouville function. A well known conjecture of Chowla asserts that for any distinct natural numbers

CARMICHAEL NUMBERS IN ARITHMETIC PROGRESSIONS

h_1,\dots,h_k

The distribution of a p modulo one

, one has

Vinogradov's three primes theorem with almost twin primes

\sum_{1 \leq n \leq X} \lambda(n+h_1) \dotsm \lambda(n+h_k) = o(X)

Real zeros of holomorphic Hecke cusp forms and sieving short intervals

as

When the sieve works

X \to \infty

A NOTE ON SMOOTH NUMBERS IN SHORT INTERVALS

. This conjecture remains unproven for any

Another note on smooth numbers in short intervals

h_1,\dots,h_k