Some Results on Harmonic Type Sums

Abstract

In this study, we consider the summatory function of convolutions of theMöbius function with harmonic numbers, and we show that these summatoryfunctions are linked to the distribution of prime numbers. In particular, wegive infinitely many asymptotics which are consequences of the Riemannhypothesis. We also give quantitative estimate for the moment function whichcounts non-integer hyperharmonic numbers. Then, we obtain the asymptoticbehaviour of hyperharmonics.

Keywords

• möbius function
• hyperharmonic numbers
• dirichlet series
• möbius fonksiyonu
• hiperharmonik sayılar
• dirichlet serileri