Abstract :
Let image be the negative of a prime, image and image its ring of integers. Let image be a prime ideal in image of prime norm congruent to image. Under these assumptions, there exists Hecke characters image of K with conductor image and infinite type (1,0). Their L-series image are associated to a CM elliptic curve image defined over the Hilbert class field of K. We will prove a Waldspurger-type formula for image of the form image where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at N and infinity and image are class group representatives of K. An application of this formula for the case N=-7 will allow us to prove the non-vanishing of a family of L-series of level 7D over K.
