The average size of Ramanujan sums over quadratic number fields(II)

Wenguang Zhai

The average size of Ramanujan sums over quadratic number fields(II)

Number Theory 2021-09-24 v1

Authors: Wenguang Zhai

Abstract

In this paper we study Ramanujan sums $c_{\bf m}(\bf n)$ , where ${\bf m}$ and ${\bf n}$ are integral ideals in an arbitrary quadratic number field. We give some new results about the asymptotic behavior of sums of $c_{\bf m}(\bf n)$ over both ${\bf m}$ and ${\bf n}$ .

Keywords

Ramanujan sums quadratic number fields integral ideals asymptotic behavior

Cite

@article{arxiv.2109.11111,
  title  = {The average size of Ramanujan sums over quadratic number fields(II)},
  author = {Wenguang Zhai},
  journal= {arXiv preprint arXiv:2109.11111},
  year   = {2021}
}

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