On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem
arXiv:0709.3145
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.
arXiv comment11 pages, revised version