Turkish Journal of MathematicsTheorems on Three-Term Relations for Hardy Sum
Faculty of Arts and Sciences,
Department of Mathematics,
Abstract: Some three-term and mixed three-term relations for Hardy sums were given by Goldberg . His proofs are based on Bernd's transformation formulae for the logarithms of the classical Theat-functions. Pettet and Sitaramachandararo  proved elementary proofs for all of Goldberg's results and also proved some three-term relations of Dedekind sums. In this paper, some new theorems on three-term relations for hardy sums were found by applying derivative operator to three-term polynomial relation. Furthermore, proofs of the reciprocity relations for Hardy sums are presented in a more concise way from the original proofs of Berndt [2, 3, 4] and Goldberg .
Turk. J. Math., 22, (1998), 153-162.
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Other articles published in the same issue: Turk. J. Math.,vol.22,iss.2.