Talk:Dirichlet character

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Mathematics rating:	Start Class	High Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Close to B-Class. A good lead would help. Geometry guy 15:53, 10 June 2007 (UTC)

Contents 1 History 2 Missing character tables 3 Sufficient conditions 4 mod 4 character 5 mod 7 character

[edit] History

Historically, what does the L in L-function or L-series stand for? Lagrange? Ninte 11:40, 13 July 2006 (UTC)

[edit] Missing character tables

It seems obvious to me that the following tables are missing, but since I know nothing of this subject beyond what I've just read here I better check:

=== Modulus 1 ===

There are φ(1) = 1 characters modulo 1:

χ \ n	1
χ1(n)	1

=== Modulus 2 ===

There are φ(2) = 1 characters modulo 2:

χ \ n	1	2
χ1(n)	1	0

Since the text claims to present "all of the characters up to modulus 7", these should be included, no? Hv 15:52, 9 February 2006 (UTC)

Yes, that is correct. But perhaps these can continue to be left out, for, I fear, they would contribute to a mind-numbing clutter? Sometimes, less is more. linas 00:43, 10 February 2006 (UTC)

If it is clutter, maybe it'd be better to show only the table for 7 - I think the rest are pretty obvious once you understand those. I've corrected the comment at the top to promise only what is actually there. Hv 11:18, 10 February 2006 (UTC)

[edit] Sufficient conditions

I am not an expert on Dirichlet characters, but ... are we sure that the first and third conditions really are sufficient? - Doesn't the identically zero function satisfy the first and third conditions, whilst not being a Dirichlet character? Madmath789 21:21, 26 June 2006 (UTC)

It appears someone cleaned up the article already linas 04:04, 9 July 2006 (UTC)

[edit] mod 4 character

Just wondering something... of the two mod 4 characters on this page, the first {1,0,1,0} seems to be the same as the sole mod 2 character {1,0}. Does it really need to be in the list twice? I think it should be deleted from the mod 4 list, considering its period is 2; that would leave the sole mod 4 character as {1,0,-1,0}.

Bird of paradox 09:34, 29 September 2006 (UTC)

I don't think it would be correct to remove it, as that would make it appear as if there were really only one character mod 4. There is a theorem about the number of characters mod n, and it tells us that there are 2 mod 4 characters - it just happens that one of them is the same as the only mod 2 character. Madmath789 09:41, 29 September 2006 (UTC)

[edit] mod 7 character

There was an error in this table which I have corrected. The error set ω = exp(πi / 6) but as a circle is 2π radians this should be ω = exp(πi / 3) Wilmot1 08:04, 19 July 2007 (UTC)