On a generalization of arithmetic functions and the Ramanujan sums

Yusuke Fujisawa

On a generalization of arithmetic functions and the Ramanujan sums

Number Theory 2014-04-29 v2

Authors: Yusuke Fujisawa

Abstract

Let $K$ be a number field. This paper considers arithmetic functions over $K$ , that are, complex valued functions on the set of nonzero integral ideals in $K$ . Firstly we generalize some basic results on arithmetic functions. Next we define the generalized Ramanujan sums over $K$ and show some properties.

Keywords

ramanujan identities and series special functions exponential sums

Cite

@article{arxiv.1212.1864,
  title  = {On a generalization of arithmetic functions and the Ramanujan sums},
  author = {Yusuke Fujisawa},
  journal= {arXiv preprint arXiv:1212.1864},
  year   = {2014}
}

Comments

This paper has been withdrawn. The author noticed that this paper was not good

Related papers

View all related →