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

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

2007-09-20

arxiv.org/abs/0709.3145v2

Mathematics

Number Theory

11 pages, revised version

Scientific paper

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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