The normal number of prime factors of fa(n)
نویسنده
چکیده
Assuming a quasi-generalized Riemann Hypothesis (6) for certain Dedekind zeta functions, we prove the following theorem: If a ≥ 2 is a square-free integer, then for the exponent function f a (n) (defined below) we have n≤x (a,n)=1 (Ω(f a (n)) − 1 2 (log log n) 2) 2 ≪ x(log log x) 3. This implies that the function Ω(f a (n)) has " normal order " 1 2 (log log n) 2 .
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