Arithmetic Incidence Functions : A Study of Factorability

TL;DRAbstract

In terminology of number theory, an arithmetic incidence function can be characterized as a function that possesses all the defining properties of both an incidence function and an arithmetic function of two variables. Under this characterization, a complex valued function f of two variables defined on the set of positive integers is an arithmetic incidence function if f(x,y) = 0 whenever the element x does not preceed the element y, where the order is determined by the standard ordering of positive integers. 
\n
\nAny suborder of the standard ordering of the positive integers determines a subclass of arithmetic incidence functions specific to that suborder. This thesis concentrates on the subclass which is determined by the divisibility ordering of positive integers. The primary objective is to present arithmetic incidence functions as a natural generalization of arithmetic functions of one variable, and to generalize the associated notions of multiplicativity and complete mul

Chat with Paper

AI Agents for this Paper