Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms

Alexandru Ciolan, Alessandro Languasco, Pieter Moree

In 1961, Rankin determined the asymptotic behavior of the number $S_{k,q}(x)$ of positive integers $n\le x$ for which a given prime $q$ does not divide ${\sigma }_k(n),$ the $k$-th divisor…