Hi Frederic, I believe that the name Gross-Zagier L-function is not standard. At least I had to go and look in the code to find out what its definition is. So the documentation should probably include a description of the definition.
Now to your question: The function is L_A(E,s) depending on an elliptic curve E/Q and an ideal class A in an imaginary quadratic field. The functional equation for it is (0.2) on page 267 of Gross-Zagier. You are asking what value of "conductor" you have to feed Dokchitser's implementation. Comparing the two and making sure the same normalisations are used, one should be able to get the answer. If I did it right, I get that the value is N^2 |D|^2/4 where N is the conductor of the elliptic curve and D is the discriminant of the quadratic field. (which may be 4*d). But I may be wrong. (I am actually surprised it is independend of A.) In any case, the function check_functional_equation should tell you if you got it right. Chris On 12 May 2015 at 14:15, <[email protected]> wrote: > Hello again, > > well, in fact what should be the correct conductor (level ?) in full > generality is not clear to me at all. So an expert help is really required ! > > input : An elliptic curve of conductor N, and the imaginary number field > Q(\sqrt(-d)) > > wanted: a formula involving N and d for the "conductor" for the > Gross-Zagier L-function attached to the input. Could it be just always > N*N*d*d ? or sometimes N*N*d*d/4 ? > > Should I ask that in MathOverflow ? > > Frederic > > Le samedi 2 mai 2015 20:24:51 UTC+2, [email protected] a écrit : >> >> Hello, >> >> I think I managed to find the problem myself. The conductor was divided >> by 4 for no special reason.. >> So this is now working. If somebody is interested to test.. >> >> Frédéric >> >> Le samedi 2 mai 2015 18:30:55 UTC+2, [email protected] a écrit : >>> >>> Dear number theorists, >>> >>> To avoid thinking about some other things, I have been fighting with >>> ticket #4606, dealing with "Gross-Zagier L-function" attached to a pair >>> (E,A) where >>> E is an elliptic curve over Q and A an ideal class in a quadratic >>> (imaginary?) number field. >>> >>> I am now in the state where the Dirichlet coefficients of the wanted >>> L-function are computed correctly, but still the numerical answer is wrong. >>> So I was wondering if maybe the parameters given to Dokchister may be >>> wrong. >>> If somebody here could help, that would be great ! Or maybe forward this >>> question to somebody knowing the answer? >>> >>> http://trac.sagemath.org/ticket/4606 >>> >>> The parameters are in the file src/sage/modular/modform/l_series.py >>> >>> thanks a lot, >>> >>> Frédéric >>> >> -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-nt. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
