Meromorphic modular form

A meromorphic modular form obeys the modular transformation law and is meromorphic on the upper half-plane and at the cusps.

Table of contents
- Valence formula for the modular group Meromorphic modular form

Valence formula for the modular group

For a nonzero meromorphic modular form

f

k

,

v_{\infty} (f) + \frac{1}{2} v_{i} (f) + \frac{1}{3} v_{ρ} (f) + \sum_{z \neq = i, ρ} v_{z} (f) = \frac{k}{12}, ρ = e^{2 πi /3},

where the sum takes one representative from each modular-group orbit.

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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 137 / 3 / b / Solution

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