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

Abstract

Given two arithmetical functions $f,g$ we derive, under suitable conditions, asymptotic formulas with error term, for the convolution sums ${\sum }_{n\le N}f(n)g(n+h)$, 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.

To appear in Journal of Number Theory

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