Xavier Roblot on Thu, 22 Oct 2015 14:18:54 +0200

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Re: GP interface for computing Artin L functions

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.