Let E be an elliptic curve defined over Q. Suppose it has complex multiplication by an order of an imaginary quadratic extension K/Q and p is a prime of good ordinary reduction. Also, suppose that the sign of functional equation of L(E,s) is 1 and p splits in K. Accordingly, the anticyclotomic Katz padic Lfunction vanishes. Is there a version of padic Gross  Zagier formula for the two variable Katz padic Lfunction in this case? The results of Perrin  Riou seem to exclude this choice of imaginary quadratic extension.
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Is there complex Gross  Zagier in this case? Their work also excludes this case. If there is, one can expect the padic height of that Heegner point to appear in padic version, as in the case of Perrin  Riou. There is a paper of Conrad on complex Gross  Zagier which includes this case. However, I do not know whether complex version follows from that paper. Probably some more work in needed. 

