Some Results on Harmonic Type Sums
Abstract
In this study, we consider the summatory function of convolutions of the Möbius function with harmonic numbers, and we show that these summatory functions are linked to the distribution of prime numbers. In particular, we give infinitely many asymptotics which are consequences of the Riemann hypothesis. We also give quantitative estimate for the moment function which counts non-integer hyperharmonic numbers. Then, we obtain the asymptotic behaviour of hyperharmonics.
Keywords
Möbius function,hyperharmonic numbers,Dirichlet series
Thanks
We thank to the anonymous referee for the suggestions which improved the quality of the paper.
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