This research demonstrates a new reciprocal relation for generalized dedekind sums, indicating implications for bernoulli polynomials and dirichlet functions.
UDC 517.5 We mainly generalize a reciprocal relation in the inverse form, namely, S(2h̄, m, n, k)+S(2k̄, 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 s₅(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.
No takes yet. Share an insight, caveat, or question.
Luo et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: