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Prime number theorem

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Reference no: EM13660

1. For r € IR, show that  855_Prime Number Theorem.png

2. Weknow that the Dirichlet series  2331_Prime Number Theorem1.pngconverges 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 479_Prime Number Theorem3.png

For r ∈ IR, show that 588_Prime Number Theorem4.png

4. Prove that the existence of

423_Prime Number Theorem5.png

implies the Prime Number Theorem.

5. For r ∈ lR, we know that

1944_Prime Number Theorem6.png

Use this to prove that

1313_Prime Number Theorem7.png

6. Let p > 2 be a prime. Prove from first principles that

1466_Prime Number Theorem8.png

Reference no: EM13660

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