Abstract
Let
H
λ
4
be the Hecke group
x
,
y
:
x
2
=
y
4
=
1
and, for a square-free positive integer
n
, consider the subset
ℚ
∗
−
n
=
a
+
−
n
/
c
|
a
,
b
=
a
2
+
n
/
c
∈
ℤ
,
c
∈
2
ℤ
of the quadratic imaginary number field
ℚ
−
n
. Following a line of research in the relevant literature, we study the properties of the action of
H
λ
4
on
ℚ
∗
−
n
. In particular, we calculate the number of orbits arising from this action for every such
n
. Some illustrative examples are also given.