My c++ L-function package has a general L-function class and library of
functions.
Given basic data for the L-function (Dirichlet series coefficients and
functional equation) it can compute the function.
The command line interface, lcalc, has some basic built in types of L-functions
(including Dirichlet L-functions). It would be possible to access more of the
library from
within sage and have more L-functions accessible. I agree with William that it
would
make sense to work on it at SAGE Days 11.
Mike
On Tue, 28 Oct 2008, William Stein wrote:
> 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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