Generating functions and generalized Dedekind sums

نویسنده

  • Ira M. Gessel
چکیده

We study sums of the form ∑ ζ R(ζ), where R is a rational function and the sum is over all nth roots of unity ζ (often with ζ = 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 ∏ ζ(1− xR(ζ)). Multisection can be used to evaluate some simple, but important sums. Finally, the method of partial fractions reduces the evaluation of arbitrary generalized Dedekind sums to those of a very simple form.

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عنوان ژورنال:
  • Electr. J. Comb.

دوره 4  شماره 

صفحات  -

تاریخ انتشار 1997