On certain aspects of the M\"obius randomness principle
We study different aspects of the Möbius randomness principle. We rephrase the Chowla and Sarnak conjectures and the Riemann hypothesis for abstract sequences and study their relationship. In particular, we show that in this setting the Chowla and Sarnak conjectures do not imply the Riemann hypothesis. We also study the connections between the multiplicative and additive van der Corput criteria.