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TY - CHAP
TI - GENERALIZATIONS
A2 - RADEMACHER, HANS
A2 - GROSSWALD, EMIL
AB - 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 summand*μ*is restricted by congruence conditions. These types of Dedekind sums are in full generality contained in the definition

$s(h,k;x,y) = \sum\limits_{\mu \bmod k} {\left( {\left( {\frac{{\mu + y}}{k}} \right)} \right)} \left( {\left( {h\frac{{\mu + y}}{k} + x} \right)} \right)$

where*x*and*y*

EP - 65
ET - 1
PB - Mathematical Association of America
PY - 1972
SN - 9780883850480
SP - 64
T2 - Dedekind Sums
UR - http://www.jstor.org/stable/10.4169/j.ctt5hh823.9
VL - 16
Y2 - 2021/07/26/
ER -