Dedekind sum

In mathematics, Dedekind sums are certain finite sums of products of a sawtooth function. Dedekind introduced them in the 1880's to express the functional equation of the Dedekind eta function, in a commentary to Bernhard Riemann's collected papers.. They have subsequently been much studied in number theory but also occur in some results in topology, geometric combinatorics, algebraic geometry, and computational complexity. Dedekind sums have been generalized in various directions, satisfying a large number of functional equations; this article lists only a small fraction of these.

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