# On partial sums of arithmetical functions of two variables with absolutely convergent Ramanujan expansions

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## Abstract

In this article, we derive an asymptotic formula for the sums of the form \({\sum }_{n_{1},n_{2}\le N}f(n_1,n_2)\) with an explicit error term, for any arithmetical function *f* of two variables with absolutely convergent Ramanujan expansion and Ramanujan coefficients satisfying certain hypothesis.

## Keywords

Arithmetic functions Ramanujan expansions Ramanujan sums asymptotic formula## 2010 Mathematics Subject Classification

11N37 11A25 11K65## Notes

### Acknowledgements

The author would like to thank Prof. M. Ram Murty for his valuable remarks and suggestions during the preparation of this article. She is also grateful to the referee for going through the manuscript meticulously and for the useful suggestions to improve the quality of the paper.

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