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Bill Allombert on Fri, 06 Jan 2023 19:53:45 +0100
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Re: bnrL1 output ordering
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- To: pari-users@pari.math.u-bordeaux.fr
- Subject: Re: bnrL1 output ordering
- From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
- Date: Fri, 6 Jan 2023 19:52:37 +0100
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On Fri, Jan 06, 2023 at 07:30:58PM +0100, Pierre Charollois wrote:
> Hello,
>
> I am using the nice command bnrL1 these days;
> it returns the values of L functions for all characters modulo a given
> conductor, but
> I struggle to understand how the ordering for the output works. Is the
> trivial character given first ? last ? What's the rule if the class group
> group/its dual is a product of cyclic groups ?
You should use the flag 2^3=8 'return also the characters.'
Alternatively, you can use the lfun interface and specify the order of the
characters yourself.
> Also, I am more inclined towards partial zeta values; is there a specific
> command for that (and thus a "natural" ordering for class group elements
> that you have in mind ) ?
No but I have gp scripts for that. It depends which partial zeta values you are
interested in.
Are you interested by the Dirichlet series which is the sum over all ideals in a
gievn ideal class ?
Cheers,
Bill.