Asymptotic distribution of normalized arithmetical functions

Asymptotic Distribution of Normalized Arithmetical Functions

Let f(n) be an arbitrary arithmetical function and let A N and B N be sequences of real numbers with 0< B N . + oe with N. We give a sufficient condition for (f(n)-AN)/BN to have a limiting distribution. The case when f(n) is defined by f(n ) = Zg(d), where the summation is over all divisors d of n and g(d) is any given arithmetical function, is discussed in more detail . A concrete example is ...

Arithmetical Functions I: Multiplicative Functions

Truth be told, this definition is a bit embarrassing. It would mean that taking any function from calculus whose domain contains [1,+∞) and restricting it to positive integer values, we get an arithmetical function. For instance, e −3x cos2 x+(17 log(x+1)) is an arithmetical function according to this definition, although it is, at best, dubious whether this function holds any significance in n...

Fourier Expansions of Arithmetical Functions

q-DEFORMATION OF ARITHMETICAL FUNCTIONS

Asymptotic Distribution of Divergence Measure with Applications