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Valence formula for the modular group
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)
Mathematics
Area of mathematics
Number theory
Modular form
Meromorphic modular form
2026-09-24
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For
a
nonzero
meromorphic modular form
f
of
weight
k
,
v
∞
(
f
)
+
2
1
v
i
(
f
)
+
3
1
v
ρ
(
f
)
+
∑
z
=
i
,
ρ
v
z
(
f
)
=
12
k
,
ρ
=
e
2
πi
/3
,
(1)
where the
sum
takes one representative from each
modular-group
orbit
.
Ancestors
(6)
Meromorphic modular form
Modular form
Number theory
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 137
/
3
/
b
/
Solution
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