Hello May I dare ask : is it possible that there is a problem in formula (0.2) of Gross-Zagier ? I do not manage to make sense of the powers of pi and 2.
As far as I can see, there should be 4 gamma factors (0,0,1,1), weight 2, and the conductor should be N**2 * D**2 But there are some spurious 2 and pi factors. As it is this does not fit into Dokchister setting.. Frederic Le mercredi 13 mai 2015 10:06:43 UTC+2, [email protected] a écrit : > > 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]> 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.
