Michael Th. Rassias, László Tóth
Published 2015-12-04Version 1
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.
Comments: To Professor Helmut Maier on his 60th birthday. In: Analytic Number Theory - In Honor of Helmut Maier's 60th Birthday, C. Pomerance and M. Th. Rassias (eds.), Springer, New York, 2015, pp. 329--343
The Discrete Fourier Transform of $\mathbf{(r,s)-}$even functions
The discrete Fourier transform of $r$-even functions
Integral representations of q-analogues of the Hurwitz zeta function
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