modular function
C51322
concept
A modular function is a complex-valued function on the upper half-plane that is invariant under the action of a modular group (typically SL(2,ℤ)) and is meromorphic on the extended upper half-plane, including at the cusps.
All labels observed (3)
| Label | Occurrences |
|---|---|
| inner function | 1 |
| modular form | 1 |
| modular function canonical | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: modular function
Generated description
A modular function is a complex-valued function on the upper half-plane that is invariant under the action of a modular group (typically SL(2,ℤ)) and is meromorphic on the extended upper half-plane, including at the cusps.
Instances (3)
| Instance | Via concept surface |
|---|---|
| modular j-invariant | — |
|
Blaschke products
surface form:
Blaschke product
|
inner function |
| Eisenstein series | modular form |