Unbounded Renormalisations: Preliminary Results

Abstract

At the present time a central problem in the probabilistic theory of numbers is to determine when a given additive function f(n) may be renormalised by functions α(x) and β(x) so that as x → ∞ the frequencies

$$v_x (n;\frac{{f(n) - \alpha (x)}}{{\beta (x)}} \leqslant z)$$

((1))

possess a weak limit.