Abstract
1. 1. We denote by
r (n)
the number of representations of
n
as the sum of two squares, representations which differ only in sign or order being counted as distinct; or, what is the same thing, the number of integral solutions of
u
2
+
v
2
, (1. 11) or the coefficient of
z
n
in the expansion (
D
(
z
) )
2
= (1 + 2
z
+ 2
z
4
+ 2
z
9
+ ...)
2
= Ʃ
∞
0
r (n)
z
n
. (1. 12) If
x
is not an integer, or is negative, we write
r (x)
= 0.
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