The Birch and Swinnerton-Dyer conjecture is a conjecture about the form of the first non-vanishing derivative of the Hasse-Weil L-function of an elliptic curve at $s= 1$, expressed in terms of a higher regulator, analogous to the class number formula for a Dedekind zeta function.
This is hence a conjecture about special values of L-functions. It influenced the more far-reaching Beilinson conjectures.
Wikipedia, Birch and Swinnerton-Dyer conjecture
Frank Gounelas, The BSD cconjecture, regulators and special values of L-functions (pdf)
Spencer Bloch, A note on height pairings, Tamagwawa numbers, and the Birch and Swinnerton-Dyer conjecture, Inventiones math. 58, 65-76 (1980) (pdf)
Conrad, Venkatesh, et al., BSD Seminar Introduction to the BSD conjecture, All lecture notes
Last revised on July 15, 2018 at 10:43:48. See the history of this page for a list of all contributions to it.