On analytic properties and character analogs of Hardy sums (Q1025707)

The author studies properties of the arithmetical sum \(Y(h,k)= 4ks_5(h,k)\), where \(s_5(h,k)\) is a classical Hardy sum and \(h,k\) are coprime integers with \(k\) positive. Residue calculus is used to prove a reciprocity law relating \(Y(h,k)\) and \(Y(k,h)\). Elementary methods are then used to derive further properties, including a representation in terms of Dirichlet characters and generalized Bernoulli numbers.