Results 31 to 40 of about 17,724,358 (326)

On a certain class of arithmetic functions [PDF]

Mathematica Bohemica, 2017
A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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New properties of arithmetic functions related to gcd and lcm [PDF]

Notes on Number Theory and Discrete Mathematics
This paper explores additional properties of the arithmetic functions f_α(n) and g_α(n), defined respectively by f_α(n)=Πʳᵢ₌₁pᵢ^{(eᵢ,α)} and g_α(n)=Πʳᵢ₌₁pᵢ^{[eᵢ,α]}, where n=Πʳᵢ₌₁pᵢ^eᵢ is the prime factorization of a positive integer n>1, (a,b) and [a,b]
Brahim Mittou
doaj   +1 more source

New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

Axioms, 2023
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms.
Hsien-Chung Wu
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Characterizations of L-additive functions via generalized arithmetic convolutions [PDF]

Notes on Number Theory and Discrete Mathematics
This paper investigates the properties of L-additive functions within the algebraic frameworks of two generalized arithmetic convolutions: the K-convolution and Narkiewicz's A-convolution.
Champak Talukdar, Debashis Bhattacharjee, Helen K. Saikia   +2 more
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Two arithmetic functions related to Euler's and Dedekind's functions [PDF]

Notes on Number Theory and Discrete Mathematics
Two new arithmetic functions are introduced. In some sense, they are modifications of Euler's and Dedekind's functions. Some properties of the new functions are studied.
Krassimir Atanassov
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A Functional Equation in Arithmetic [PDF]

Transactions of the American Mathematical Society, 1936
which occurs in all theories of numerical functions hitherto considered. The two most highly developed theories of this kind are those in which multiplication in the ring of all numerical functions is abstractly identical with C (Cauchy) or D (Dirichlet) multiplication of infinite series.t Lehmer's five postulates are sufficient for the development of ...
openaire   +2 more sources

Multidimensional local theorem in the Knopfmachers semigroup

Lietuvos Matematikos Rinkinys, 2007
In the presentpaper a multidimensionallocal theorem for arithmetic functions definedin the Knopfmachers semigroup G is obtained.
Rimantas Skrabutėnas
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Divisibility of arithmetic functions [PDF]

Pacific Journal of Mathematics, 1984
A derivative-like operator on the Dirichlet ring of arithmetic functions is used to develop formulas for the greatest common divisor of certain arithmetic functions. It is conjectured that formulas of this type hold more generally.
openaire   +2 more sources

The mean value of the function d(n)/d*(n) in arithmetic progressions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Let d(n) and d*(n) be, respectively, the number of divisors and the number of unitary divisors of an integer n≥1. A divisor d of an integer is to be said unitary if it is prime over n/d.
Ouarda Bouakkaz, Abdallah Derbal
doaj   +1 more source

Arithmetic of function field units [PDF]

, 2015
We introduce the module of Stark units associated to a Drinfeld module defined over the ring of integers of a global function field. We investigate the arithmetic properties of these objects, and as an application, we prove a “discrete analogue” for ...
B. Anglès, Floric Tavares Ribeiro
semanticscholar   +1 more source