43 research outputs found
The identical equations of the multiplicative function
This article does not have an abstract
Quasi-boolean algebras and many-valued logics
This article does not have an abstract
Contributions to the theory of apolarity
“I am the holder of a Scholarship from the University of Madras and one from the Madras Government. Also of a grant from the British Department of Scientific Research.” -- Caree
The apolar invariant of bilinear forms
This article does not have an abstract
The Localisation theory in set-topology
This article does not have an abstract
Sums of products of Ramanujan sums
The Ramanujan sum is defined as the sum of -th powers of the
primitive -th roots of unity. We investigate arithmetic functions of
variables defined as certain sums of the products
, where are polynomials with
integer coefficients. A modified orthogonality relation of the Ramanujan sums
is also derived.Comment: 13 pages, revise
Arithmetical properties of Multiple Ramanujan sums
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.Comment: 19 page
On continuous functions of a real variable
This article does not have an abstract
On disjunction in intuitionist logic
This article does not have an abstract