Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:item
|
| gptkbp:analyzes |
modular curves
|
| gptkbp:are_functions_on |
the upper half-plane
|
| gptkbp:are_invariant_under |
the action of modular group
|
| gptkbp:can_be_computed_using |
modular symbols
|
| gptkbp:can_be_generalized_to |
p-adic modular forms
|
| gptkbp:can_transform_into |
modular transformations
|
| gptkbp:constructed_in |
modular forms of higher weight
new forms from old forms |
| gptkbp:example |
automorphic forms
|
| gptkbp:has_applications_in |
gptkb:crypt
|
| gptkbp:have_a_fourier_expansion |
atcus points
|
| https://www.w3.org/2000/01/rdf-schema#label |
classical modular forms
|
| gptkbp:is_analyzed_in |
the theory of modular forms with complex multiplication
|
| gptkbp:is_associated_with |
L-functions
automorphic representations modular forms of half-integral weight the theory of modular forms with complex multiplication |
| gptkbp:is_connected_to |
Hecke algebras
the Langlands program the theory of modular functions the theory of modular forms with rational coefficients the theory of modular forms in characteristic p the theory of modular forms with level structure |
| gptkbp:is_described_as |
new invariants in algebraic geometry
new types of modular forms |
| gptkbp:is_essential_for |
the study of rational points on curves
the study of the Birch and Swinnerton-Dyer conjecture |
| gptkbp:is_linked_to |
partition theory
|
| gptkbp:is_related_to |
gptkb:crypt
Galois representations the theory of modular forms over finite fields the theory of modular forms over number fields the theory of modular forms in arithmetic geometry the theory of modular forms with level raising |
| gptkbp:is_represented_in |
q-series
linear combinations of basis forms |
| gptkbp:is_studied_for |
the arithmetic of elliptic curves
the Galois action on the cohomology of modular curves the arithmetic of modular forms. |
| gptkbp:is_studied_in |
algebraic geometry
representation theory the context of algebraic topology the theory of modular forms with integral coefficients |
| gptkbp:is_used_in |
gptkb:string_theory
number theory the study of special values of L-functions the proof of Fermat's Last Theorem the study of the Langlands correspondence |
| gptkbp:scientific_classification |
gptkb:weight
gptkb:editor cusp forms |
| gptkbp:bfsParent |
gptkb:Siegel_modular_forms
|
| gptkbp:bfsLayer |
6
|