Arithmetical properties of Multiple Ramanujan sums

Details Arithmetical properties of Multiple Ramanujan sums Arithmetical properties of Multiple Ramanujan sums

2007-01-19

arxiv.org/abs/math/0701528v1

Ramanujan J. 21 (2010), 241-261

Mathematics

Number Theory

19 pages

Scientific paper

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.

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