Göral, HaydarSertbaş, Doğa Can2023-04-102023-04-1020202148-2446http://doi.org/10.29130/dubited.622285https://search.trdizin.gov.tr/yayin/detay/389953https://hdl.handle.net/20.500.12684/11592In 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 giveinfinitely many asymptotics which are consequences of the Riemann hypothesis. We also give quantitativeestimate for the moment function which counts non-integer hyperharmonic numbers. Then, we obtain theasymptotic behaviour of hyperharmonics.en10.29130/dubited.622285info:eu-repo/semantics/openAccessArticle81642653389953