We introduce some new higher dimensional generalizations of the Dedekind sums associated with the Bernoulli functions and of those Hardy sums which are defined by the sawtooth function. We generalize a variant of Parseval’s formula for the discrete Fourier transform to derive finite trigonometric representations for these sums in a simple unified manner. We also consider a related sum involving the Hurwitz zeta function.
CITATION STYLE
Rassias, M. T., & Tóth, L. (2015). Trigonometric representations of generalized dedekind and hardy sums via the discrete fourier transform. In Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday (pp. 329–343). Springer International Publishing. https://doi.org/10.1007/978-3-319-22240-0_20
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