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
DOI: 10.2140/pjm.1975.57.339
Abstract

The object of the paper is to evaluate

∑ r=0a−1[b(r+ x) ---a--- − y][c(r+ x) --a---- − z]
+ ∑ s=0b−1[c(s + y) ---b--- − z][a(s+ y) ---b--- − x]
+ ∑ t=0c−1[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