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SUMMARY:Quadratic twists of elliptic curves - John Coates (Cambridge)
DTSTART:20140225T161500Z
DTEND:20140225T171500Z
UID:TALK49716@talks.cam.ac.uk
CONTACT:James Newton
DESCRIPTION:In the family of all quadratic twists of an elliptic curve def
 ined over Q\, it has long been folklore that one expects that\, amongst al
 l twists with root number +1 (resp. root number -1)\, those whose complex 
 L-function does not vanish at s=1 (resp. whose complex L-function has a si
 mple zero at s=1) should have density 1. This has never been proven for a 
 single elliptic curve over Q\, but recently Y. Tian discovered a new metho
 d for making important progress in this direction for the quadratic twists
  of the elliptic curve y^2^ = x^3^ - x. In my lecture\, I shall discuss jo
 int work with Y. Li\, Y. Tian and S. Zhuai which makes some first steps to
 wards extending Tian's method to the quadratic twists of a large family of
  elliptic curves over Q. Some of our results also generalize an old lemma 
 due to B. Birch.
LOCATION:MR13
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