Trigonometric Representations of Generalized Dedekind and Hardy Sums via the Discrete Fourier Transform

Michael Th. Rassias () and László Tóth ()
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Michael Th. Rassias: ETH-Zürich, Department of Mathematics
László Tóth: University of Pécs, Department of Mathematics

A chapter in Analytic Number Theory, 2015, pp 329-343 from Springer

Abstract: Abstract 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.

Keywords: Dedekind sums; Hardy sums; Bernoulli polynomials and functions; Hurwitz zeta function; Discrete Fourier transform; 11F20; 11L03 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_20

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DOI: 10.1007/978-3-319-22240-0_20

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