RECIPROCITY RELATIONS OF UNIPOLY-DEDEKIND SUMS
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Recently, Kim et al. introduced the poly-Dedekind sums associated with the type 2 poly-Bernoulli functions of index k and the poly-Dedekind sums associated with the poly-Bernoulli functions of index k. In this paper, as generalizations of the Apostol’s generalized Dedekind sums, we introduce two kinds of unipoly-Dedekind sums. One is the unipoly-Dedekind sums that replaces the type 2 poly-Bernoulli functions of arbitrary indices in poly-Dedekind sums by the type 2 unipoly- Bernoulli functions of arbitrary indices, and we derive the reciprocity relation for these. The other is the unipoly-Dedekind sums that replaces the poly-Bernoulli functions of arbitrary indices in poly- Dedekind sums by the unipoly-Bernoulli functions of arbitrary indices, and we derive the reciprocity relation for these.
Abstract
Recently, Kim et al. introduced the poly-Dedekind sums associated with the type 2 poly-Bernoulli functions of index k and the poly-Dedekind sums associated with the poly-Bernoulli functions of index k. In this paper, as generalizations of the Apostol’s generalized Dedekind sums, we introduce two kinds of unipoly-Dedekind sums. One is the unipoly-Dedekind sums that replaces the type 2 poly-Bernoulli functions of arbitrary indices in poly-Dedekind sums by the type 2 unipoly- Bernoulli functions of arbitrary indices, and we derive the reciprocity relation for these. The other is the unipoly-Dedekind sums that replaces the poly-Bernoulli functions of arbitrary indices in poly- Dedekind sums by the unipoly-Bernoulli functions of arbitrary indices, and we derive the reciprocity relation for these.
참고문헌 (22)
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