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arXiv · 0709.3145

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

R. M. Abrarov·S. M. Abrarov
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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.

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R. M. Abrarov, S. M. Abrarov. 2007-09-24. On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem. https://arxiv.org/abs/0709.3145

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