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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:On the p-part of the Birch–Swinnerton-Dyer conject
ure for elliptic curves with CM by the ring of int
egers of Q(√−3) - Yukako Kezuka University of Camb
ridge
DTSTART;TZID=Europe/London:20141128T150000
DTEND;TZID=Europe/London:20141128T160000
UID:TALK56526AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56526
DESCRIPTION:We study an infinite family of quadratic and cubic
twists of the elliptic curve E parametrised by th
e\nmodular curve X0(27). There are two main result
s\, both of which support the validity of the famo
us Birch–\nSwinnerton-Dyer conjecture. One of them
concerns the 2-adic valuation of the algebraic pa
rt of the L-series\nof quadratic twists of E evalu
ated at 1\, and the other concerns the 3-adic valu
ations of the L-series of cubic\ntwists of E at 1.
We check that the bounds obtained in the main res
ults are precisely the bounds predicted\nby the co
njecture\, with equality holding when the Tate–Sha
farevich groups of the curves are trivial.
LOCATION:CMS\, MR4
CONTACT:Julian Brough
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