Lecture 16

Question 1

If A(x) = ∑_(n≤x) µ(n)/n

What relation imples the prime number theorem

Answer 1

A(x) = o(1) as x → ∞

Question 2

Let F be a real or complex valued function defined on (0,+∞) and let G(x) = log x ∑_(n≤x) F (x/n) .
Then what does

• F(x) log x + ∑_(n≤x) F (x/n) Λ(n) =

Answer 2

= ∑_(d≤x) µ(d)G(x/d)