Hello, thanks a lot. I was suspecting something like that. I have to look at the code now.
And indeed, "Gross-Zagier L-functions" does not seem to be a standard name for these L-functions. Frederic Le mardi 12 mai 2015 17:17:10 UTC+2, chris wuthrich a écrit : > > 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] <javascript:>> 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] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> 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.
