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SUMMARY:The Birch and Swinnerton-Dyer conjectural formula - Robert Miller 
 (Warwick)
DTSTART:20101116T161500Z
DTEND:20101116T171500Z
UID:TALK27807@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:The Birch and Swinnerton-Dyer conjecture (BSD) asserts the equ
 ality of\nthe rank of the Mordell-Weil group of an elliptic curve to the o
 rder\nof vanishing of its L-function at 1. The conjectural formula posits 
 a\nrelationship between the leading coefficient of the L-function at 1\nan
 d several arithmetic and analytic constants associated to the curve\,\ninc
 luding the order of the Tate-Shafarevich group\, which is\nconjectured to 
 be finite. If the analytic rank of a curve over Q is at\nmost 1\, then the
 re is an algorithm to compute this order and hence\nprove the conjecture. 
 The aim of this talk is to describe this\nalgorithm in detail and report o
 n the progress of proving BSD for\nspecific elliptic curves of this type.\
 n
LOCATION:MR13
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