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 twopoint correlations of the Möbius function and the twin prime conjecture, in view of recent parity breaking results of K. Matomäki, M. Radziwi l l and T. Tao.