Nonlinear Analysis (Mar 2020)

Modeling the Dirichlet distribution using multiplicative functions

  • Gintautas Bareikis,
  • Algirdas Mačiulis

DOI
https://doi.org/10.15388/namc.2020.25.16518
Journal volume & issue
Vol. 25, no. 2

Abstract

Read online

For q,m,n,d ∈ N and some multiplicative function f > 0, we denote by T3(n) the sum of f(d) over the ordered triples (q,m,d) with qmd = n. We prove that Cesaro mean of distribution functions defined by means of T3 uniformly converges to the one-parameter Dirichlet distribution function. The parameter of the limit distribution depends on the values of f on primes. The remainder term is estimated as well.

Keywords