About a forty years old conjecture by P. Erdős

Abstract

In connection with a characterization ofc logn within the class of additive arithmetic functions, i.e. such thatf (mn)=f(m)+f(n), which has been conjectured by P. Erdős in 1946 and is still unproved, we outline some subsequent researches involving various tools and standpoints, and we report some expressive results either lying close to that conjecture or revealing a similar spirit.