2 citations · 3 across the 5 of their papers we have counts for
5 papers
Multivariate arithmetical functions and vector calculus
Yusuke Fujisawa
The motivation of this paper is to construct the theory of vector calculus of multivariate arithmetical functions. We prove analogues of integral theorems and Poincare's lemma.
On Mobius and Liouville functions of order
Yusuke Fujisawa
Let be a number field, a positive integer. In this paper, we define the Mobius and Liouville functions of order in . We give a formula about the partial sums of them…
On sums of generalized Ramanujan sums
Yusuke Fujisawa
Ramanujan sums have been studied and generalized by several authors. For example, Nowak studied these sums over quadratic number fields, and Grytczuk defined that on semigroups. In…
On partial sums of the Möbius and Liouville functions for number fields
Yusuke Fujisawa, Makoto Minamide
Landau examined the partial sums of the Möbius function and the Liouville function for a number field . First we shall try again the same problem by using a new Perron's formula…
On a generalization of arithmetic functions and the Ramanujan sums
Yusuke Fujisawa
Let be a number field. This paper considers arithmetic functions over , that are, complex valued functions on the set of nonzero integral ideals in . Firstly we generaliz…