Birch and Swinnerton-Dyer conjecture
GPTKB entity
Statements (60)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:has_a_focus_on |
numerical experiments
|
| gptkbp:has_connection_to |
Galois representations
|
| gptkbp:has_implications_for |
gptkb:crypt
the theory of modular forms |
| https://www.w3.org/2000/01/rdf-schema#label |
Birch and Swinnerton-Dyer conjecture
|
| gptkbp:ingredients |
1960s
|
| gptkbp:involves |
L-functions
|
| gptkbp:is_a_conjecture_about |
the distribution of rational points
|
| gptkbp:is_a_conjecture_that |
has not been resolved
|
| gptkbp:is_a_conjecture_that_has |
wide-ranging implications in mathematics
|
| gptkbp:is_a_conjecture_that_has_inspired |
numerous research projects
|
| gptkbp:is_a_conjecture_that_involves |
the analytic properties of L-functions
|
| gptkbp:is_a_subject_of |
mathematicians worldwide
|
| gptkbp:is_associated_with |
Mordell-Weil theorem
|
| gptkbp:is_connected_to |
rank of an elliptic curve
|
| gptkbp:is_considered_a_key_problem_in |
arithmetic geometry
|
| gptkbp:is_debated_in |
the subject of many mathematical discussions
analyzed using computational methods discussed in various mathematical forums the basis for many mathematical explorations the basis for many mathematical explorations. the basis for many theoretical advancements the focus of international research collaborations the focus of many Ph D theses the focus of many mathematical inquiries the focus of many mathematical studies the foundation for many mathematical theories the subject of collaborative research efforts the subject of extensive numerical analysis the subject of many conferences the subject of many mathematical analyses the subject of many mathematical debates the subject of many mathematical investigations the subject of many mathematical workshops the topic of many mathematical lectures the topic of many seminars |
| gptkbp:is_discussed_in |
contemporary research papers
|
| gptkbp:is_essential_for |
understanding rational points
|
| gptkbp:is_linked_to |
the Tate-Shafarevich group
|
| gptkbp:is_often_referenced_in |
mathematical literature
|
| gptkbp:is_one_of |
gptkb:Millennium_Prize_Problems
|
| gptkbp:is_part_of |
number theory
|
| gptkbp:is_recommended_by |
the number of rational points is finite if L(1) is zero
the number of rational points is infinite if L(1) is non-zero |
| gptkbp:is_related_to |
gptkb:crypt
the Langlands program Heights on elliptic curves the conjecture of Mordell |
| gptkbp:is_significant_for |
the study of Diophantine equations
|
| gptkbp:is_still_unproven |
true or false status
|
| gptkbp:is_studied_in |
algebraic geometry
|
| gptkbp:is_tested_for |
many specific elliptic curves
|
| gptkbp:issues |
rational solutions
|
| gptkbp:named_after |
gptkb:Bryan_Birch
gptkb:Peter_Swinnerton-Dyer |
| gptkbp:proposed_by |
relationship between the number of rational points on an elliptic curve and the behavior of its L-function
|
| gptkbp:topics |
modern mathematics
|
| gptkbp:bfsParent |
gptkb:Automorphic_forms
|
| gptkbp:bfsLayer |
6
|