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math.NT2015
On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions
Su Hu, Daeyeoul Kim, Min-Soo Kim
The Apostol-Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper…
math.CA2015★ 16 cited
Special values and integral representations for the Hurwitz-type Euler zeta functions
Su Hu, Daeyeoul Kim, Min-Soo Kim
The Hurwitz-type Euler zeta function is defined as a deformation of the Hurwitz zeta function: \begin{equation*} ζ_E(s,x)=\sum_{n=0}^\infty\frac{(-1)^n}{(n+x)^s}. \end{equation*} I…