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\noindent {\bf Ira Gessel}\bigskip\noindent
Generating Functions and Generalized Dedekind Sums"
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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 {\it 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 {\it factorization\/} applies if we have an explicit formula 
for $\prod_\zeta (1-xR(\zeta))$. {\it Multisection\/} can be used to
evaluate some simple, but important sums. Finally, the method of 
{\it partial fractions\/} reduces the evaluation of arbitrary
 generalized Dedekind sums to those of a very
simple form.
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