Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
modular group
|
| gptkbp:alsoKnownAs |
gptkb:modular_discriminant
|
| gptkbp:cuspForm |
true
|
| gptkbp:definedIn |
Δ(z) = q ∏_{n=1}^∞ (1 - q^n)^{24}, where q = e^{2πiz}
|
| gptkbp:discoveredBy |
gptkb:Srinivasa_Ramanujan
|
| gptkbp:field |
complex analysis
modular forms number theory |
| gptkbp:firstNonzeroTerm |
q
|
| gptkbp:FourierCoefficient |
τ(n)
|
| gptkbp:FourierExpansion |
Δ(z) = ∑_{n=1}^∞ τ(n)q^n
|
| gptkbp:holomorphic |
true
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ramanujan's Delta function
|
| gptkbp:level |
1
|
| gptkbp:modularGroup |
gptkb:SL(2,ℤ)
|
| gptkbp:relatedTo |
gptkb:Eisenstein_series
gptkb:modular_discriminant Hecke operators L-functions modular group modular forms of weight 12 |
| gptkbp:subjectOf |
gptkb:Ramanujan_conjecture
gptkb:Ramanujan_tau_function |
| gptkbp:symbol |
Δ(z)
|
| gptkbp:vanishesAt |
infinity
|
| gptkbp:weight |
12
|
| gptkbp:bfsParent |
gptkb:Ramanujan_tau_function
|
| gptkbp:bfsLayer |
6
|