Arithmetical properties of Multiple Ramanujan sums
Number Theory
2012-12-07 v1
Abstract
In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic properties of the multiple Ramanujan sum and study several types of Dirichlet series involving the multiple Ramanujan sum. As an application, we evaluate higher-dimensional determinants of higher-dimensional matrices, the entries of which are given by values of the multiple Ramanujan sum.
Cite
@article{arxiv.math/0701528,
title = {Arithmetical properties of Multiple Ramanujan sums},
author = {Yoshinori Yamasaki},
journal= {arXiv preprint arXiv:math/0701528},
year = {2012}
}
Comments
19 pages