Lecture 15

Question 1

lim_(x→∞) M(x)/x = 0

What is this equivalent to and what is M(x)

Answer 1

• Equivalent to the prime number theorem
• M(x) = ∑_(n≤x) µ(n).

Question 2

M(x) = o(x) as x → ∞

What does this imply

Answer 2

ψ(x) ∼ x as x → ∞