A new form of the reciprocal relation for generalized Dedekind sums

• Date: 2026
• Main Authors: Luo, Shiyuan, Xu, Zhefeng
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2026
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8522
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We mainly generalize a reciprocal relation in the inverse form, namely,  $$S(2\overline{h}, m, n, k)+S(2\overline{k}, m, n, h)$$ for the generalized Dedekind sums by using the Fourier expansions of the Bernoulli polynomials and  analytic methods. Further, the reciprocal relation for genera...