On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions
Su Hu, Daeyeoul Kim, Min-Soo Kim
TL;DR
This paper derives a reciprocity formula for the Apostol-Dedekind sum involving quasi-periodic Euler functions, expanding the understanding of these sums through the Boole summation formula.
Contribution
It introduces a reciprocity formula for the Apostol-Dedekind sum with quasi-periodic Euler functions using the Boole summation formula, extending previous work on Dedekind sums.
Findings
Reciprocity formula established for the sum
Application of Boole summation formula to Euler functions
Enhanced understanding of generalized Dedekind sums
Abstract
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, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Advanced Combinatorial Mathematics