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- Q527863 subject Q6248542.
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- Q527863 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 2014, 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).".
- Q527863 thumbnail BSD_data_plot_for_elliptic_curve_800h1.svg?width=300.
- Q527863 wikiPageExternalLink mmm061024.pdf.
- Q527863 wikiPageExternalLink birchswin.pdf.
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- Q527863 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.".
- Q527863 label "Birch and Swinnerton-Dyer conjecture".
- Q527863 depiction BSD_data_plot_for_elliptic_curve_800h1.svg.