SeminarsOn the non-vanishing of central L-values of canonical CM elliptic curves with quadratic twists
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Let K be an imaginary quadratic field of discriminant D. In this talk, we consider canonical elliptic curves with CM by K and of global root number one. These curves are defined over the Hilbert class field of K and their Galois conjugates are isogenous to each other. We prove the central L-values of these canonical CM elliptic curves twisted by quadratic characters of conductor d are positive whenever the D is sufficiently large than d. This result extends previous works of Rohrlich, Villegas and Tonghai Yang to include even discriminant D.
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Pin-Chi Hung
2013-10-04
10:30:00 - 11:30:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)
Let K be an imaginary quadratic field of discriminant D. In this talk, we consider canonical elliptic curves with CM by K and of global root number one. These curves are defined over the Hilbert class field of K and their Galois conjugates are isogenous to each other. We prove the central L-values of these canonical CM elliptic curves twisted by quadratic characters of conductor d are positive whenever the D is sufficiently large than d. This result extends previous works of Rohrlich, Villegas and Tonghai Yang to include even discriminant D.