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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
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 Maddede Bu Makale
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Amaç & Hipotez:In this paper, we present the character analogue of the Boole summationformula.
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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
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