Statements (74)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:are_periodic_in |
two directions
|
| gptkbp:are_used_to_construct |
gptkb:crypt
|
| gptkbp:can_be_expressed_in_terms_of |
elliptic integrals
|
| gptkbp:can_be_generalized_to |
higher dimensions
|
| gptkbp:can_be_used_to_solve |
gptkb:Mathematics
|
| gptkbp:can_transform_into |
modular transformations
|
| gptkbp:constructed_in |
modular forms
|
| gptkbp:defined_in_terms_of |
complex variables
|
| gptkbp:developed_by |
the heat equation
|
| gptkbp:has_applications_in |
mathematical physics
number theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Jacobi's theta functions
|
| gptkbp:is_connected_to |
the theory of partitions
partition functions the theory of Riemann theta functions |
| gptkbp:is_essential_for |
the study of dynamical systems
the study of combinatorial geometry the study of integrable systems the study of mathematical logic the study of complex manifolds the study of computational mathematics the study of mathematical physics the theory of q-series the study of algorithm design |
| gptkbp:is_related_to |
gptkb:series
gptkb:Riemann_surfaces Bessel functions the theory of Lie algebras the theory of stochastic processes the theory of hypergeometric functions the theory of modular forms and elliptic curves the theory of random matrices the theory of machine learning the theory of algebraic functions the theory of coding theory theta functions of other types |
| gptkbp:is_represented_in |
infinite series
linear combinations of exponentials products of sine functions solutions to certain differential equations |
| gptkbp:is_studied_in |
complex analysis
|
| gptkbp:is_used_in |
gptkb:crypt
gptkb:quantum_field_theory gptkb:string_theory gptkb:statistical_mechanics signal processing the study of algebraic geometry the study of algebraic topology the study of asymptotic analysis the study of combinatorial identities the study of modular equations the study of modular forms the theory of automorphic forms the theory of special functions the study of chaos theory the study of optimization problems the study of quantum mechanics the study of graph theory the study of mathematical modeling the study of mathematical analysis the study of artificial intelligence the study of control theory the study of differential geometry the study of functional equations the study of numerical analysis the study of information theory the study of data analysis |
| gptkbp:named_after |
gptkb:Carl_Gustav_Jacob_Jacobi
|
| gptkbp:related_to |
modular forms
|
| gptkbp:satisfy |
functional equations
|
| gptkbp:used_in |
theory of elliptic functions
|
| gptkbp:bfsParent |
gptkb:Theta_series
|
| gptkbp:bfsLayer |
5
|