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

Abstract

For two arithmetical functions $f$ and $g$ with absolutely convergent Ramanujan expansions, Murty and Saha have recently derived asymptotic formulas with error term for the convolution sum ${\sum }_{n\le N}f(n)g(n+h)$ under some suitable conditions (see http://arxiv.org/abs/1506.01945). In this follow up article we improve these results with a weakened hypothesis which is in some sense minimal.

References in corpus (1)

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

Cited by in corpus (3)

• Finite Ramanujan expansions and shifted convolution sums of arithmetical functions
• Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II
• Sieve functions in arithmetic bands, II