Stable martingale central limit theorem for multiplicative functions with prime variance parameter
Let f∈Mf\in\mathcal{M}f∈M. Suppose that … for some θ∈(0,1)\theta\in(0,1)θ∈(0,1), and that there exists c>0c>0c>0 such that ∣f(pk)∣2=O(2k(1−c))|f(p^k)|^2=O(2^{k(1-c)})∣f(pk)∣2=O(2k(1−c)) and ∣f(p)∣<1/c|f(p)|<1/c∣f(p)∣<1/c for all k≥2k\geq 2k≥2 and primes ppp.…