Some Results on Harmonic Type Sums
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 hypothe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Düzce University
2020-01-01
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| Series: | Düzce Üniversitesi Bilim ve Teknoloji Dergisi |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/946485 |
| Summary: | 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. |
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| ISSN: | 2148-2446 |