On Tue, Oct 28, 2008 at 2:26 AM, John Cremona <[EMAIL PROTECTED]> wrote:
>
> This is an excellent idea. Obviously, for every package Sage
> includes, as much of its functionality as possible should be made
> available ! But this does take time and effort.
>
> I am CC-ing this to sage-nt since if we are going to discuss how to do
> this in detail that might be the best forum.
>
This would probably be a good project for Mike Rubinstein and
I, who will both be at Sage Days 11 in Austin, TX.
(Mike: see below.)
> John
>
> 2008/10/28 Pablo De Napoli <[EMAIL PROTECTED]>:
>>
>> Hi,
>>
>> I'm reading the notes of William's talk "Three Lectures about Explicit
>> Methods in Number Theory Using Sage", that are indeed very interesting.
>>
>> It comments that Sage includes functionallity to compute the zeros of
>> L-series
>> of elliptic curves, by doing
>>
>> sage: E = EllipticCurve('389a1')
>> sage: L = E.lseries()
>>
>> sage: L.zeros(10)
>> [0.000000000, 0.000000000, 2.87609907, 4.41689608, 5.79340263,
>> 6.98596665, 7.47490750, 8.63320525, 9.63307880, 10.3514333]
>>
>> It comments that
>> " Rubinstein's program can also do similar computations for a wide class
>> of L-functions, though not all of this functionality is as easy to use from
>> Sage as for elliptic curves."
>>
>> It would be nice to functionallity for computing other L-functions that
>> appears in number theory. The most basic one would: compute the L-series
>> associated with a Dirichlet character, and been able to do some simmilar
>> computation like
>>
>> sage: G=DirichletGroup(10)
>> sage: c=G[1]
>> sage: L=c.lseries()
>> sage: L.zeros(10)
>>
>> Also one could like to do similar computations for instance with Dedekind
>> zeta
>> function of a number fileld, something like...
>>
>> sage: K.<sqrt2> = QuadraticField(2)
>> sage: Z.DedekindZeta()
>> sage: Z.zeros(10)
>>
>> Would it be possible to implement such a functionallity in Sage?
>> Perhaps we would need a more more flexible class for representing L-series.
>>
>> best regards
>> Pablo
>>
>>
>> >
>>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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