Bill Allombert on Mon, 13 Sep 2021 15:46:46 +0200 |
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Re: L-functions of ray class fields |
On Mon, Sep 13, 2021 at 03:13:21PM +0200, Markus Grassl wrote: > Hello, > > I am starting to explore the functionality to evaluate L-functions of ray > class fields in PARI. > > Consider the following example: > > ? K=bnfinit(y^2-17); > ? R=bnrinit(K,[idealmul(K,2,idealprimedec(K,67)[1]),[1,0]]); > ? bnrL1(R,,6) ... > First, it seems as if the function bnrL1 was single-threaded, while lfun > used multiple cores. Indeed this is the case. > Is there a simple way to use multi-threading? Could you clarify ? Do you mean, to have bnrL1 use multithreading ? it is not done yet. On the other hand you can use lfun with a vector of characters if it is that you had in mind. > I tried to directly evaluate the L-functions, e.g. > > ? lfun(lfuncreate([R,[1]]),0,1) > %7 = 0.90384905518988545678200390170972794465 - > 2.3724351853612471172697035833485504030*I > > But this does not remove the Euler factors, which I request above by setting > the third bit of the flag. > Is there a simple way to define the L-function with the Euler factors > removed so that I can get particular values as they would be returned by > bnrL1? No, because such imprimitive functions do not satisfy the functional equation. But you can multiply by the Euler factors afterward. Cheers, Bill