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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, the reciprocity formulas for two new arithmetic sums,arising from the summation formulas, and for Hardy--Berndt sum $S_{p}(b,c:\chi)$ are proved.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we present the character analogue of the Boole summationformula.
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Key Findings & Data:Using this formula, an integral representation is derived for thealternating Dirichlet $L$-function and its derivative is evaluated at $s=0$.Some applications of the character analogue of the Boole summation formula andthe integral representation are given about the alternating Dirichlet $L$-function.
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Conclusion & Impact:Moreover, the reciprocity formulas for two new arithmetic sums,arising from the summation formulas, and for Hardy--Berndt sum $S_{p}(b,c:\chi)$ are proved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Boole summation formula · Dirichlet $L$-function · Hardy--Berndt sum
Abstract
In this paper, we present the character analogue of the Boole summationformula. Using this formula, an integral representation is derived for thealternating Dirichlet $L$-function and its derivative is evaluated at $s=0$.Some applications of the character analogue of the Boole summation formula andthe integral representation are given about the alternating Dirichlet $L$-function. Moreover, the reciprocity formulas for two new arithmetic sums,arising from the summation formulas, and for Hardy--Berndt sum $S_{p}(b,c:\chi)$ are proved.
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Cite This Article
CAN, M., DAĞLI, M. C. (2017). Character analogue of the Boole summation formula with applications. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 5, 1204–1223. https://ajindex.com/articles/723163