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

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

Number Theory 2016-08-05 v1

Authors: 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.

Keywords

Ramanujan expansions arithmetical functions error term asymptotic formula convolution sums Parseval type formula

Cite

@article{arxiv.1506.01945,
  title  = {On the error term in a Parseval type formula in the theory of Ramanujan expansions},
  author = {M. Ram Murty and Biswajyoti Saha},
  journal= {arXiv preprint arXiv:1506.01945},
  year   = {2016}
}

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To appear in Journal of Number Theory

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

Abstract

Keywords

Cite

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