Vol. 57, No. 2, 1975

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A three-term relation for some sums related to Dedekind sums

L. Carlitz

Vol. 57 (1975), No. 2, 339–348
Abstract

The object of the paper is to evaluate

r=0a1[b(r+ x)
---a--- y][c(r+ x)
--a---- z]
+ s=0b1[c(s + y)
---b--- z][a(s+ y)
---b--- x]
+ t=0c1[a(t+ z)
-------
c x][b(t+ z)
-------
c y].
where [u] is the greatest integer function,
(b,c) = (c,a) = (a,b) = 1.

and

0 ≦ x < 1,0 ≦ y < 1,0 ≦ z < 1.

Mathematical Subject Classification
Primary: 10A20
Milestones
Received: 31 October 1974
Published: 1 April 1975
Authors
L. Carlitz