On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem

Abstract

We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understand better the properties of these numbers and their asymptotic behavior. On the basis of these identities a simple proof of the Prime Number Theorem is represented.

11 pages, revised version

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• Riemann Hypothesis may be proved by induction