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Dergiler / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 3

Higher-order character Dedekind sum

Mümün CAN
Sayfa
998–1015
Yayın Tarihi
2022-11-04
DOI
—
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Moreover, we offer Petersson–Knopp type identities for this sum.

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Amaç & Hipotez:In this paper, we are interested in higher-order character Dedekind sum $sum_{v=0}^{ck;-1};X_1;(nu);{mathfrak B}_{p,;x_2};left(afrac{v;+;z}c+xright);+;{mathfrak B}_q;left(bfrac{v;+;z}{ck}+yright);,;a,;b,;c;in;mathbb{N};and;x,;y,;z;in;mathbb{R}$ where χ1 and χ2 are primitive characters of modulus k, Bp (x) and Bp,χ2(x) are Bernoulli and generalized Bernoullifunctions, respectively.
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Temel Bulgular & Veri:We employ the Fourier series technique to demonstrate reciprocity formulas for this sum.
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Sonuç & Katkı:Moreover, we offer Petersson–Knopp type identities for this sum.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we are interested in higher-order character Dedekind sum $sum_{v=0}^{ck;-1};X_1;(nu);{mathfrak B}_{p,;x_2};left(afrac{v;+;z}c+xright);+;{mathfrak B}_q;left(bfrac{v;+;z}{ck}+yright);,;a,;b,;c;in;mathbb{N};and;x,;y,;z;in;mathbb{R}$ where χ1 and χ2 are primitive characters of modulus k, Bp (x) and Bp,χ2(x) are Bernoulli and generalized Bernoullifunctions, respectively. We employ the Fourier series technique to demonstrate reciprocity formulas for this sum. Derivedformulas are analogues of Mikolás’ reciprocity formula. Moreover, we offer Petersson–Knopp type identities for this sum.

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Bu Makaleye Atıf Yap

CAN, M. (2022). Higher-order character Dedekind sum. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 998–1015. https://ajindex.com/articles/607514

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Kaynakça (19)

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