Pierre Charollois on Fri, 06 Jan 2023 21:12:47 +0100

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Re: bnrL1 output ordering

Thanks Bill !

I am indeed interested in Dirichlet series that are the sum over ideals in a given ideal class (including a sign character) for complex cubic fields.

Best regards,

Le ven. 6 janv. 2023 à 19:52, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> a écrit :
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 ?