Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
Ma, Yuankui, Kim, Dae San, Lee, Hyunseok, Kim, Hanyoung, Kim, Taekyun
ADVANCES IN DIFFERENCE EQUATIONS, 2021, Vol.2021 No.1
- 주제(키워드) 도움말 Poly-Dedekind type DC sums , Poly-Genocchi polynomials , Poly-Euler polynomials , Poly-Euler functions , 11F20 , 11B68 , 11B83
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- 발행년도 2021
- 총서유형 Journal
- 본문언어 영어
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- The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind-type DC sums, which are obtained from the Dedekind-type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.
- The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind-type DC sums, which are obtained from the Dedekind-type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.
