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

M. Ram Murty; Biswajyoti Saha

doi:10.1016/j.jnt.2015.04.026

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arXiv · 1506.01945

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

M. Ram Murty·Biswajyoti Saha

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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.

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M. Ram Murty, Biswajyoti Saha. 2015-06-05. On the error term in a Parseval type formula in the theory of Ramanujan expansions. https://doi.org/10.1016/j.jnt.2015.04.026

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