A new form of the reciprocal relation for generalized Dedekind sums - Luo, Shiyuan; Xu, Zhefeng (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5 We mainly generalize a reciprocal relation in the inverse form, namely, S(2h, m, n, k)+S(2k, 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 generalized Hardy sums s_5(h,m,k) is also derived. Moreover, we unexpectedly obtain a computational formula for one kind of the mean value of Dirichlet L-functions with the weight given by even character sums.