Abstract
For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the sum \({\sum }_{n \le N} f(n)\) with explicit error term. As a corollary we obtain new results about sum-of-divisors functions and Jordan’s totient functions.
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Acknowledgements
The author would like to thank M. Ram Murty for numerous valuable discussions and remarks while preparing this article and for bringing some important references to the author’s notice. He would also like to thank Sanoli Gun for going through an earlier version of the article and for her important comments. He also thanks the referee for his/her comments.
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SAHA, B. Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions. Proc Math Sci 126, 295–303 (2016). https://doi.org/10.1007/s12044-016-0291-6
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DOI: https://doi.org/10.1007/s12044-016-0291-6