Average order of arithmetic functions

On the Normal Order of Arithmetic Functions.

On the Average Order of Some Arithmetical Functions

We consider a large class of arithmetical functions generated by Dirichlet series satisfying a functional equation with gamma factors. Our objective is to state some 12 results for the average order of these arithmetical functions. Our objective here is to state some B-theorems on the average order of a class of arithmetical functions. We indicate very briefly the class of arithmetical function...

On the Reversed Average Intensity Order

Based on the increasing property of ratio of average reversed hazard rates of two non-negative random variables a new stochastic order for the sake of comparison of two lifetime distributions is proposed. This stochastic order admits some distinguishing properties. In order to illustrate the obtained results, a semi-parametric model which is called reverse hazard power and a mixture model of pr...

On Average Bit Complexity of Interval Arithmetic

In many practical situations, we know only the intervals which contain the actual (unknown) values of physical quantities. If we know the intervals x for a quantity x and y for another quantity y, then, for every arithmetic operation , the set of possible values of x y also forms an interval; the operations leading from x and y to this new interval are called interval arithmetic operations. For...

On the Average Order of Ideal Functions and Other Arithmetical Functions

We consider a large class of arithmetical functions generated by Dirichlet series satisfying a functional equation with gamma factors. We state a general O-theorem for the average order of these arithmetical functions and apply the result to ideal functions of algebraic number fields. Landau [4] and Chandrasekharan and Narasimhan [3] have proved O-theorems for the average order of a large class...