(Answered) Dirichlet

Engineering

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) : 346_Prime Number Theorem2.png

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

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