On the error term in a Parseval type formula in the theory of Ramanujan expansions

Given two arithmetical functions f, g   we derive, under suitable conditions, asymptotic formulas with error term, for the convolution sums ∑n≤Nf(n)g(n+h)∑n≤Nf(n)g(n+h), building on an earlier work of Gadiyar, Murty and Padma. A key role in our method is played by the theory of Ramanujan expansions for arithmetical functions.