#4606: elliptic curves -- implement gross-Zagier L-functions
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Reporter: robertwb | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.7
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: William Stein, | Reviewers:
Robert Bradshaw, Craig Citro | Work issues:
Report Upstream: N/A | Commit:
Branch: u/chapoton/4606 | 0bb47fa2466dbc64485237c788b964e5b0280ccb
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'William Stein, Robert Bradshaw, Craig Citro',
'oldvalue': ''}):
* author: => William Stein, Robert Bradshaw, Craig Citro
Old description:
> Make it so one can do:
> {{{
> sage: e = EllipticCurve('37a')
> sage: K.<a> = QuadraticField(-40)
> sage: A = K.class_group().gen(0); A
> Fractional ideal class (2, -1/2*a)
> sage: L = e.lseries_gross_zagier(A)
> sage: L(2)
> 0
> sage: L.taylor_series(2,5)
> nobody has seen this!
> }}}
New description:
Make it so one can do:
{{{
sage: e = EllipticCurve('37a')
sage: K.<a> = QuadraticField(-40)
sage: A = K.class_group().gen(0); A
Fractional ideal class (2, -1/2*a)
sage: L = e.lseries_gross_zagier(A)
sage: L(1)
0.000000000000000
sage: L.taylor_series(1,5)
0.000000000000000 - 5.51899839494458*z + 13.6297841350649*z^2 -
16.2292417817675*z^3 + 7.94788823722712*z^4 + O(z^5)
}}}
nobody had seen this!
--
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Ticket URL: <http://trac.sagemath.org/ticket/4606#comment:30>
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