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CATEGORIES:Number Theory Seminar
SUMMARY:Quadratic twists of elliptic curves - John Coates
(Cambridge)
DTSTART;TZID=Europe/London:20140225T161500
DTEND;TZID=Europe/London:20140225T171500
UID:TALK49716AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/49716
DESCRIPTION:In the family of all quadratic twists of an ellipt
ic curve defined over Q\, it has long been folklor
e that one expects that\, amongst all twists with
root number +1 (resp. root number -1)\, those whos
e complex L-function does not vanish at s=1 (resp.
whose complex L-function has a simple zero at s=1
) should have density 1. This has never been prove
n for a single elliptic curve over Q\, but recentl
y Y. Tian discovered a new method for making impor
tant progress in this direction for the quadratic
twists of the elliptic curve y^2^ = x^3^ - x. In m
y lecture\, I shall discuss joint work with Y. Li\
, Y. Tian and S. Zhuai which makes some first step
s towards 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 lemm
a due to B. Birch.
LOCATION:MR13
CONTACT:James Newton
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