Lecture----数学院晨兴数学中心

Title:	Quadratic twists of X_0(49) VII
Speaker:	Prof. John Coates (Cambridge Univ.)
Time:	2015-6-24, 10:45-11:45
Place:	N817
Abstract:	The quadratic twists of X_0(49) are the only elliptic curves defined over Q for which the prime 2 is potentially ordinary. For reasons which we still do not understand fully, this makes their Iwasawa theory more accessible, especially at the prime 2. In the course, I hope to prove the conjecture of Birch and Swinnerton-Dyer for the quadratic twists of X_0(49), whose complex L-series does not vanish at s=1, concentrating in particular on the difficult 2-primary part of the exact Birch-Swinnerton-Dyer formula for the order of the Tate-Shafarevich group of such a twist. In the discussion of the formula for the 2-primary part, I will be following work of Gonzalez-Aviles.
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