## Dedekind Sum

Given Relatively Prime Integers and , the Dedekind sum is defined by

 (1)

where
 (2)

Dedekind sums obey 2-term
 (3)

and 3-term
 (4)

reciprocity laws, where , , are pairwise Coprime and
 (5) (6) (7)
Let , , , with (i.e., are pairwise Relatively Prime), then the Dedekind sums also satisfy

 (8)

where , and , are any Integers such that (Pommersheim 1993).

References

Pommersheim, J. Toric Varieties, Lattice Points, and Dedekind Sums.'' Math. Ann. 295, 1-24, 1993.