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 ? Cheers, Bill.