A note on correlations of arithmetic functions

Abstract

In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's conjecture for two-point correlations of the Möbius function and the twin prime conjecture, in view of recent parity breaking results of K. Matomäki, M. Radziwiłł and T. Tao.