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<p>We define a unification of the generalized Dedekind–Rademacher sum introduced by Hall, Wilson and Zagier and generalized Hardy–Berndt sums introduced by Can. These sums involve higher order Apostol–Bernoulli polynomials and functions. We prove its reciprocity formula which contains all of the reciprocity formulae in the literature for generalized Dedekind and Hardy–Berndt sums as special cases.</p>

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Reciprocity formulae for generalized Dedekind and Hardy–Berndt sums involving Apostol–Bernoulli polynomials and functions

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Brad Isaacson

摘要

We define a unification of the generalized Dedekind–Rademacher sum introduced by Hall, Wilson and Zagier and generalized Hardy–Berndt sums introduced by Can. These sums involve higher order Apostol–Bernoulli polynomials and functions. We prove its reciprocity formula which contains all of the reciprocity formulae in the literature for generalized Dedekind and Hardy–Berndt sums as special cases.