Dedekind sums - an algebraic approach. (English) Zbl 0659.10006
The author gives an explicit formula for the Dedekind sum s(d,c) in terms of the continued fraction of the ratio c/d. This formula is derived from the well-known properties of these sums. It is then shown that these properties can in fact be rederived directly from this explicit expression. Also, based on the explicit formula, closed form expressions for the sums are given when c is in certain residue classes modulo d.
Reviewer: J.L.Hafner
MSC:
11A25 | Arithmetic functions; related numbers; inversion formulas |
11A55 | Continued fractions |
11F11 | Holomorphic modular forms of integral weight |