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Turkish Journal of Mathematics

Authors

MÜMÜN CAN

DOI

10.3906/mat-1911-93

Abstract

In this paper, we are interested in higher-order character Dedekind sum% \[ \sum\limits_{v=0}^{ck-1}\chi_{1}\left( v\right) \mathcal{B}_{p,\chi_{2}% }\left( a\frac{v+z}{c}+x\right) \mathcal{B}_{q}\left( b\frac{v+z}% {ck}+y\right) ,\text{ }a,b,c\in\mathbb{N} \text{ and }x,y,z\in\mathbb{R}, \] where $\chi_{1}$ and $\chi_{2}$ are primitive characters of modulus $k,$ $\mathcal{B}_{p}\left( x\right) $ and $\mathcal{B}_{p,\chi_{2}}\left( x\right) $ are Bernoulli and generalized Bernoulli functions, respectively. We employ the Fourier series technique to demonstrate reciprocity formulas for this sum. Derived formulas are analogues of Mikolas' reciprocity formula. Moreover, we offer Petersson--Knopp type identities for this sum.

First Page

998

Last Page

1015

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