Bill Allombert on Thu, 22 Oct 2015 14:50:06 +0200

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Re: GP interface for computing Artin L functions

On Thu, Oct 22, 2015 at 02:18:41PM +0200, Xavier Roblot wrote:
> Hi Bill, 
> > We just added to master a new function lfunartin() to compute
> > Artin L functions.
> > This is based on a GP script by Charlotte Euvrard.
> > Currently, the representation needs to be given explicitly
> > 
> > This is the documentation:
> > 
> > lfunartin(nf,gal,M,n):
> > 
> >   Returns the Ldata structure associated to the Artin L-function associated to the
> > representation  rho of the Galois group of the extension K/Q,  defined over the cyclotomic field
> > Q(zeta_n),   where  nf is the nfinit structure associated to K,  gal is the galoisinit structure
> > associated to K/Q, and M is the vector of the image of the generators G.gen by rho. The elements
> > of  M  are matrices with polynomial entries,  whose variable is understood as the complex number
> > exp(2 i Pi/n).
> This is great news and that will be very useful! Do you think it could be
> possible to also specify a finite set of prime ideals of K (maybe by
> providing an integral ideal of K) that should be excluded from the Euler
> product defining the L-function? This kind of L-functions are very often used
> in the context of Stark conjectures. 

Does such L functions satisfy a functional equation compatible with the lfun
interface ?