@inbook{10.4169/j.ctt5hh823.9,
ISBN = {9780883850480},
URL = {http://www.jstor.org/stable/10.4169/j.ctt5hh823.9},
abstract = {We shall close this presentation of Dedekind sums with the mention of some of their generalizations. There are several in which the function ((x)), which is essentially the first Bernoulli polynomial${B_1}(y) = y - 1/2$of$y = x - [x]$, is replaced by higher Bernoulli polynomials. They play roles in special problems of partitions.In the work of C. Meyer [32], [33], but also already in some investigations by J. Lehner [29] and J. Livingood [30], certain Dedekind sums appear in which the summandμis restricted by congruence conditions. These types of Dedekind sums are in full generality contained in the definition$s(h,k;x,y) = \sum\limits_{\mu \bmod k} {\left( {\left( {\frac{{\mu + y}}{k}} \right)} \right)} \left( {\left( {h\frac{{\mu + y}}{k} + x} \right)} \right)$wherexandy},
bookauthor = {HANS RADEMACHER and EMIL GROSSWALD},
booktitle = {Dedekind Sums},
edition = {1},
pages = {64--65},
publisher = {Mathematical Association of America},
title = {GENERALIZATIONS},
volume = {16},
year = {1972}
}