Statements (55)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:has_function |
η(0) = 1
η(τ + 1) = e^{πi/12} η(τ) η(−1/τ) = (−iτ)^{1/2} η(τ) |
| gptkbp:has_property |
transformation properties
quasi-periodicity |
| gptkbp:has_relationship_with |
Jacobi theta function
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dedekind eta function
|
| gptkbp:is_applied_in |
gptkb:quantum_field_theory
gptkb:statistical_mechanics |
| gptkbp:is_connected_to |
L-functions
Elliptic functions |
| gptkbp:is_defined_by |
η(τ) = e^{πiτ/12} ∏_{n=1}^{∞} (1 -e^{2πinτ})
|
| gptkbp:is_expressed_in |
terms of modular equations
terms of q-series terms of Dedekind sums terms of Fourier series terms of infinite products terms of modular forms and elliptic curves terms of modular invariants terms of modular transformations |
| gptkbp:is_involved_in |
congruences
|
| gptkbp:is_part_of |
modular forms theory
|
| gptkbp:is_related_to |
gptkb:Riemann_surfaces
modular arithmetic algebraic topology complex analysis automorphic forms Hecke operators modular invariance theta functions automorphic representations modular curves |
| gptkbp:is_used_in |
gptkb:string_theory
algebraic geometry number theory partition theory theory of partitions conformal field theory theory of modular forms theory of elliptic curves theory of modular forms and algebraic geometry theory of modular forms and algebraic topology theory of modular forms and arithmetic geometry theory of modular forms and elliptic curves theory of modular forms and number theory theory of modular forms and representation theory theory of modular functions theory of q-series theory of modular forms and algebraic number theory |
| gptkbp:is_used_to |
count partitions
|
| gptkbp:named_after |
gptkb:Richard_Dedekind
|
| gptkbp:related_to |
modular forms
|
| gptkbp:bfsParent |
gptkb:Richard_Dedekind
|
| gptkbp:bfsLayer |
5
|