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Journals / Düzce Üniversitesi Bilim ve Teknoloji Dergisi / 2020 / Cilt: 8 - Sayı: 1

Some Results on Harmonic Type Sums

Harmonik Tipi Toplamlar Üzerine Bazı Sonuçlar

Haydar GÖRAL
Doğa Can SERTBAŞ
Pages
642–653
Publication Date
2022-10-12
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then, we obtain the asymptotic behaviour of hyperharmonics.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data:In particular, we give infinitely many asymptotics which are consequences of the Riemann hypothesis.
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Conclusion & Impact:Then, we obtain the asymptotic behaviour of hyperharmonics.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Möbius fonksiyonu · hiperharmonik sayılar · Dirichlet serileri

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.

Özet

Bu çalışmada, Möbius fonksiyonunun harmonik sayılarla konvolüsyonunun toplamsal fonksiyonunu ele alacağız ve bu toplamsal fonksiyonun asalların dağılımı ile ilişkili olduğunu göstereceğiz. Özel olarak, Riemann hipotezinin sonucu olan sonsuz çoklukta asimptotik vereceğiz. Ayrıca tamsayı olmayan hiperharmoniklerin sayaç fonksiyonunun momentleri için niceliksel bir kestirim vereceğiz. Sonra da hiperharmoniklerin asimptotik davranışını elde edeceğiz.

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Cite This Article

GÖRAL, H., SERTBAŞ, D. C. (2022). Some Results on Harmonic Type Sums. Düzce Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 8 - Sayı: 1, 642–653. https://ajindex.com/articles/494080

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References (7)

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