On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem
Abstract
Description
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
11 pages, revised version