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- Birch_and_Swinnerton-Dyer_conjecture abstract "In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. It is widely recognized as one of the most challenging mathematical problems; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof. It is named after mathematicians Bryan Birch and Peter Swinnerton-Dyer who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2012, only special cases of the conjecture have been proven correct.The conjecture relates arithmetic data associated to an elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K (Wiles 2006).".
- Birch_and_Swinnerton-Dyer_conjecture thumbnail BSD_data_plot_for_elliptic_curve_800h1.svg?width=300.
- Birch_and_Swinnerton-Dyer_conjecture wikiPageExternalLink 8533.
- Birch_and_Swinnerton-Dyer_conjecture wikiPageExternalLink mmm061024.pdf.
- Birch_and_Swinnerton-Dyer_conjecture wikiPageExternalLink birchswin.pdf.
- Birch_and_Swinnerton-Dyer_conjecture wikiPageID "435161".
- Birch_and_Swinnerton-Dyer_conjecture wikiPageRevisionID "606309461".
- Birch_and_Swinnerton-Dyer_conjecture hasPhotoCollection Birch_and_Swinnerton-Dyer_conjecture.
- Birch_and_Swinnerton-Dyer_conjecture id "4561".
- Birch_and_Swinnerton-Dyer_conjecture title "Birch and Swinnerton-Dyer Conjecture".
- Birch_and_Swinnerton-Dyer_conjecture title "Swinnerton-Dyer Conjecture".
- Birch_and_Swinnerton-Dyer_conjecture urlname "Swinnerton-DyerConjecture".
- Birch_and_Swinnerton-Dyer_conjecture subject Category:Conjectures.
- Birch_and_Swinnerton-Dyer_conjecture subject Category:Diophantine_geometry.
- Birch_and_Swinnerton-Dyer_conjecture subject Category:Millennium_Prize_Problems.
- Birch_and_Swinnerton-Dyer_conjecture subject Category:Number_theory.
- Birch_and_Swinnerton-Dyer_conjecture subject Category:University_of_Cambridge_Computer_Laboratory.
- Birch_and_Swinnerton-Dyer_conjecture subject Category:Zeta_and_L-functions.
- Birch_and_Swinnerton-Dyer_conjecture comment "In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. It is widely recognized as one of the most challenging mathematical problems; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof.".
- Birch_and_Swinnerton-Dyer_conjecture label "Birch and Swinnerton-Dyer conjecture".
- Birch_and_Swinnerton-Dyer_conjecture label "Congettura di Birch e Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Conjectura de Birch e Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Conjecture de Birch et Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Conjetura de Birch y Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Vermoeden van Birch en Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Vermutung von Birch und Swinnerton-Dyer".
- Birch_and_Swinnerton-Dyer_conjecture label "Гипотеза Бёрча — Свиннертон-Дайера".
- Birch_and_Swinnerton-Dyer_conjecture label "バーチ・スウィンナートン=ダイアー予想".
- Birch_and_Swinnerton-Dyer_conjecture label "贝赫和斯维讷通-戴尔猜想".
- Birch_and_Swinnerton-Dyer_conjecture sameAs Vermutung_von_Birch_und_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Conjetura_de_Birch_y_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Conjecture_de_Birch_et_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Congettura_di_Birch_e_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs バーチ・スウィンナートン=ダイアー予想.
- Birch_and_Swinnerton-Dyer_conjecture sameAs 버치-스위너턴다이어_추측.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Vermoeden_van_Birch_en_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Conjectura_de_Birch_e_Swinnerton-Dyer.
- Birch_and_Swinnerton-Dyer_conjecture sameAs m.02851n.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Q527863.
- Birch_and_Swinnerton-Dyer_conjecture sameAs Q527863.
- Birch_and_Swinnerton-Dyer_conjecture wasDerivedFrom Birch_and_Swinnerton-Dyer_conjecture?oldid=606309461.
- Birch_and_Swinnerton-Dyer_conjecture depiction BSD_data_plot_for_elliptic_curve_800h1.svg.
- Birch_and_Swinnerton-Dyer_conjecture isPrimaryTopicOf Birch_and_Swinnerton-Dyer_conjecture.