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arXiv · 1507.07862

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

Giovanni Coppola·M. Ram Murty·Biswajyoti Saha
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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.

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Giovanni Coppola, M. Ram Murty, Biswajyoti Saha. 2015-07-28. On the error term in a Parseval type formula in the theory of Ramanujan expansions II. https://doi.org/10.1016/j.jnt.2015.09.023

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