Group, Lie and Number Theory
The BirchSwinnertonDyer formula in the cases of analytic rank 0 and 1
For an elliptic curve E over the rationals, the BirchSwinnertonDyer conjecture predicts that (a) the rank of the MordellWeil group E(Q) equals the order of vanishing at s=1 of the Lfunction L(E,s) and that (b) the leading nonzero Taylor series coefficient of L(E,s) around s=1 is given by a formula in terms of objects associated with E (such as the order of its TateShafarevich group, etc). This talk will explain the strategy and ingredients in recent proofs of the ppart of (b) for most odd primes p when the curve E has analytic rank 0 or 1 (so (a) is also known). Speaker(s): Christopher Skinner (Princeton University)
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