Birch and Swinnerton-Dyer conjecture
This problem deals with number theory, which is considered as toughest math problems to date. Statement:The conjecture relates arithmetic data associated to an elliptic curve E over a number field K to the behavior 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
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Score0Rank#6
This problem deals with number theory, which is considered as toughest math problems to date. Statement:The conjecture relates arithmetic data associated to an elliptic curve E over a number field K to the behavior 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