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. Thanks, Xavier