Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
gptkb:Upper_half-plane
|
| gptkbp:defines |
η(τ) = e^{πiτ/12} ∏_{n=1}^∞ (1 - e^{2πinτ})
|
| gptkbp:field |
gptkb:Number_theory
gptkb:Modular_forms Complex analysis |
| gptkbp:firstAppearance |
1877
|
| gptkbp:hasFourierExpansion |
η(τ) = q^{1/24} ∏_{n=1}^∞ (1 - q^n), q = e^{2πiτ}
|
| gptkbp:hasZeros |
None in upper half-plane
|
| gptkbp:heldBy |
gptkb:Quasimodular_form
Holomorphic function Modular form of weight 1/2 Nowhere vanishing on upper half-plane |
| https://www.w3.org/2000/01/rdf-schema#label |
Dedekind eta function
|
| gptkbp:namedAfter |
gptkb:Richard_Dedekind
|
| gptkbp:relatedTo |
gptkb:Eisenstein_series
gptkb:Modular_discriminant gptkb:Jacobi_theta_function |
| gptkbp:satisfies |
Modular transformation property
|
| gptkbp:symbol |
η(τ)
|
| gptkbp:usedIn |
gptkb:Conformal_field_theory
gptkb:Monstrous_moonshine Elliptic functions Partition function |
| gptkbp:bfsParent |
gptkb:lion
|
| gptkbp:bfsLayer |
4
|