Provider: JSTOR http://www.jstor.org Database: JSTOR Content: text/plain; charset="us-ascii" TY - CHAP TI - INTRODUCTION A2 - RADEMACHER, HANS A2 - GROSSWALD, EMIL AB -

At first glance, the Dedekind sums seem to be a highly specialized subject. These sums denoted by$s(h,k)$are defined as follows: Leth, kbe integers,$(h,k) = 1$,$k \ge 1$then we set

(1)$s(h,k) = \sum\limits_{\mu = 1}^k {\left( {\frac{{h\mu }}{k}} \right)} \left( {\frac{\mu }{k}} \right)$

Here and in the following the symbol ((x)) is defined by

(2)$((x)) = \left\{ \begin{array}{l} x - [x] - 1/2 \\ 0 \\ \end{array} \right.$ifxis not an integer, ifxis an integer,

with [x] the greatest integer not exceedingx. This is the well-known sawtooth function of period 1 (see Figure 1),

which at the points of discontinuity takes the mean value between the

EP - 3 ET - 1 PB - Mathematical Association of America PY - 1972 SN - 9780883850480 SP - 1 T2 - Dedekind Sums UR - http://www.jstor.org/stable/10.4169/j.ctt5hh823.5 VL - 16 Y2 - 2021/07/30/ ER -