Artin representations, Dirichlet characters and links

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L-Functions and Modular Forms Database

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Artin representations, Dirichlet characters and links #1994

Closed sanni85 closed 5 years ago

sanni85 commented 7 years ago

Looking at 1 - dimensional Artin representations we (@pjbruin, @nmascot and me) noticed that:

the related objects box contains a link to "Corresponding Dirichlet character" while it should be "Dirichlet character $\chi_q(n,\dot)$" for consistency with other pages;
in the body of the page the Dirichlet character should be given with a link to the Dirichlet character page;
there is no link back from the L-function page to the Artin representation;
there is no link from Dirichlet characters to Artin characters (related object box).

For higher dimensional Artin representations, the determinant should be linked to a 1-dimensional Artin representation first.

nmascot commented 7 years ago

The first two points are fixed by pull request #1995 for representations of dimension 1 only (because for higher dimension, the determinant link should be to the Galois character, not the Dirichlet character, and I do not know how to do that)

jwj61 commented 7 years ago

What do you mean by the Galois character. Do you mean the corresponding 1-dimensional Artin representation?

nmascot commented 7 years ago

@jwj61 : Yes, exactly.

pjbruin commented 7 years ago

As far as I can see, the current status is as follows: a higher-dimensional Artin representation now has a link to its determinant as a 1-dimensional Artin representation. Between 1-dimensional Artin representations, Dirichlet characters and L-functions, the following links exist:

from 1-dim. Artin rep. to Dirichlet char.
from 1-dim. Artin rep. to L-function
from Dirichlet char. to L-function
from L-function to Dirichlet char.

The following links still seem to be missing (points 3 and 4 from the first comment on this page):

from Dirichlet char. to 1-dim. Artin rep.
from L-function to 1-dim. Artin rep.

For example, a link to http://localhost:37777/ArtinRepresentation/1.7.3t1.1c1 should be added on both http://localhost:37777/Character/Dirichlet/7/2 and http://localhost:37777/L/Character/Dirichlet/7/2/.

jvoight commented 6 years ago

Also, there's a link from the Artin representation to the number field in the friends but not vice versa, e.g. http://beta.lmfdb.org/ArtinRepresentation/3.229.4t5.1c1 has a friend link to http://beta.lmfdb.org/NumberField/4.0.229.1, but only at the bottom of the page are there Artin links. It's OK to have it in two places, but for consistency across pages I think the Artin L-functions should be solidly in the friends zone.

AndrewVSutherland commented 5 years ago

We should plan to address this in the Artin reps workshop in August 2019.

AndrewVSutherland commented 5 years ago

Fixed by #3258, which I will push to beta momentarily.