arXiv:0709.3145 Abstract | arXiv Analytics

arXiv:0709.3145 [math.NT]Abstract References Reviews Resources

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

Published 2007-09-20, updated 2007-09-24Version 2

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.

Comments: 11 pages, revised version

Categories: math.NT

Subjects: 11N05, 11A41

Keywords: prime number theorem, simple proof, generalized harmonic, properties, sum identities

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