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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also obtain integral representation for these sums.
📌 3 Key Takeaways
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Objective & Hypothesis:Applying character analogue of the Euler--MacLaurin summation formula to certain functions, we define sums which generalize character Hardy--Berndt sums $s_{3,p}(b,c:\chi)$ and $s_{4,p}(b,c:\chi),$ and prove the corresponding reciprocity formulas.
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Key Findings & Data:Applying character analogue of the Euler--MacLaurin summation formula to certain functions, we define sums which generalize character Hardy--Berndt sums $s_{3,p}(b,c:\chi)$ and $s_{4,p}(b,c:\chi),$ and prove the corresponding reciprocity formulas.
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Conclusion & Impact:We also obtain integral representation for these sums.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Dedekind Toplamı · Hardy-Berndt Toplamı · Bernoulli polinomu
Abstract
Applying character analogue of the Euler--MacLaurin summation formula to certain functions, we define sums which generalize character Hardy--Berndt sums $s_{3,p}(b,c:\chi)$ and $s_{4,p}(b,c:\chi),$ and prove the corresponding reciprocity formulas. We also obtain integral representation for these sums.
Özet
Euler--MacLaurin toplama formülünün karakter benzerini bazı fonksiyonlara uygulayarak, $s_{3,p}(b,c:\chi)$ and $s_{4,p}(b,c:\chi),$ karakter Hardy--Berndt toplamlarının genelleştirmeleri olan toplamlar tanımladık ve bu toplamlara karşılık gelen resiprosite formüllerini ispatladık. Ayrıca, bu toplamların integral gösterimlerini elde ettik.
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Cite This Article
Dağlı, M. C., Can, M. (2017). On reciprocity formula for certain character Hardy--Berndt sums. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 2 Sayı: 1, 133–139. https://ajindex.com/articles/1341805