Generating functions and generalized Dedekind sums

@article{Gessel1997GeneratingFA,
  title={Generating functions and generalized Dedekind sums},
  author={Ira M. Gessel},
  journal={Electron. J. Comb.},
  year={1997},
  volume={4}
}
  • I. Gessel
  • Published 1 October 1996
  • Mathematics
  • Electron. J. Comb.
We study sums of the form $\sum_\zeta R(\zeta)$, where $R$ is a rational function and the sum is over all $n$th roots of unity $\zeta$ (often with $\zeta =1$ excluded). We call these generalized Dedekind sums, since the most well-known sums of this form are Dedekind sums. We discuss three methods for evaluating such sums: The method of factorization applies if we have an explicit formula for $\prod_\zeta (1-xR(\zeta))$. Multisection can be used to evaluate some simple, but important sums… 
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