On the discrete convolution of the Liouville and Möbius functions

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

In this article we study some properties of the discrete convolution of Liouville function $S(n):={\sum }_{m_1+m_2=n}\lambda \left(m_1\right)\lambda \left(m_2\right)$, which is a Goldbach-t…