代写Number Theory (MA3Z7) Problem Sheet VII代做留学生Matlab编程

Number Theory (MA3Z7)

Problem Sheet VII

1. Show that the von Mangoldt function Λ(n) has generating function

2. Show that for −1 < x < 1,

[Hint: you may differentiate term-by-term.]

Deduce that

[Hint: d(n 2 ) is multiplicative.]

3. Show that for all N ≥ 1,

and hence that