1. For r € IR, show that 
2. Weknow that the Dirichlet series 
converges for σ > 0.
Use this to analytically contine ζ(s) to σ > 0.
Define A1(rn) : 
For σ > 0, show that 
For r ∈ IR, show that 
4. Prove that the existence of
implies the Prime Number Theorem.
5. For r ∈ lR, we know that
Use this to prove that
6. Let p > 2 be a prime. Prove from first principles that
