#5247: cuspform_lseries() computing sign of functional equation incorrectly
---------------------------+------------------------------------------------
Reporter: mabshoff | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: modular forms | Keywords:
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Sal reports: The following computation should produce identical values in
the last line:
{{{
E=EllipticCurve('37b2')
h=E.modular_form()
Lh = h.cuspform_lseries()
LE=E.lseries()
h.elliptic_curve()==E, Lh(1), LE(1)
}}}
The output is:
{{{
(True, 0, 0.725681061936153)
}}}
I'm running Sage 3.3.alpha3 of sage.math.
The problem seems to be the sign of the functional equation -- it looks
like the cuspform_lseries() incorrectly computes it to be -1, forcing the
value at s=1 to be 0. In sage/modular/modform/element.py the sign of the
functional equation fed into the Dokchister is computed by
{{{
e = (-1)**(l/2)*n.atkin_lehner_operator().matrix()[0,0]
}}}
which Gonzalo and Mark tell me is not correct.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5247>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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