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[For part I see \it B. H. Gross and \it D. B. Zagier, Invent. Math. 84, 225--320 (1986; Zbl 0608.14019).] \par Let X\sb 0(N) be the modular curve of level N and J\sb N its Jacobian, and denote by J\sp*\sb N the Jacobian of X\sb 0(N)/w\sb N where w\sb N is the Fricke involution. For a fundamental discriminant Dlt;0 and r\in \Bbb Z with D\equiv r\sp 2 (4N) we let Y\sbD,r be the corresponding Heegner divisor in J\sb N and Y\sp*\sbD,r be its image in J\sp*\sb N. Let f be a normalized newform in S\sb 2(Γ\sb 0(N)) and L(f,s) be its L-series. Suppose that the root number of L(f,s) is -1. \par The main result of the paper then states that the subspace of J\sp*\sb N(\Bbb Q)\otimes \Bbb R generated by the f-eigencomponents of all Heegner divisors (y\sp*\sbD,r)\sb f with (D,2N)=1 has dimension 1 if L'(f,1)\ne 0. \par More precisely, (y\sp*\sbD,r)\sb f=c((r\sp 2- D)/4N,r)y\sb f, where c(n,r) is the coefficient of e\sp2π i(nτ +rz) in a Jacobi form φ\sb f of weight 2 and index N corresponding to f in the sense of \it N.-P. Skoruppa and \it D. Zagier [Invent. Math. 94, 113--146 (1988; Zbl 0651.10020)] and y\sb f\in (J\sp*(\Bbb Q)\otimes \Bbb R)\sb f is independent of D and r with \langle y\sb f,y\sb f\rangle =L'(f,1)/4π \Vert φ\sb f\Vert\sp 2 (\langle⋅, ⋅\rangle=canonical height pairing).\par This result is in accordance with the conjectures of Birch and Swinnerton-Dyer which in the above situation (i.e. under the assumption \textord\sbs=1L(f,s)=1) would predict that \dim (J\sp*\sb N(\Bbb Q)\otimes \Bbb R)\sb f=1.
