Talk:Kronecker symbol

Something more intuitive needed?=

Untitled

Could we have something more intuitive here i.e. what does the Kronecker symbol mean?

Something similar is needed for the Jacobi and Legendre symbols too.

Johnbibby 18:19, 20 January 2007 (UTC)[reply]

The Legendre symbol gives a fairly definite meaning (whether a is a residue for a prime p). The Jacobi symbol doesn't have an intuitive meaning (IIRC, the usual meaning is that it is defined for all odd n, has the same value as the Legendre symbol whenever n is prime, and can be efficicently calculated). Does the Kronecker symbol have meaning like the Jacobi symbol except with the word "odd" removed? Ralphmerridew 00:15, 2 June 2007 (UTC)[reply]

The Kronecker's symbol is related to the real-valued Dirichlet characters (p2d3p -- March 6, 2008). —Preceding unsigned comment added by P2d3p (talk • contribs) 01:37, 7 March 2008 (UTC)[reply]

An error here =

"These extensions suffice to define the Kronecker symbol for all integer values n." Not true; there was no definition for given n = 0. —Preceding unsigned comment added by 209.67.107.10 (talk) 00:32, 10 September 2008 (UTC) <-Seems to be fixed now[reply]

Still no definition for (0/-1)

I still see no definition for (0/-1), but I assume it should be 1, which is consistent with (-1/0)=1—GraemeMcRae^talk 15:24, 4 March 2009 (UTC)[reply]

Damn, yet another missing case. I couldn't find any decent source, it seems that cases involving 0 are generally overlooked. But at least the available implementations use the convention (0|−1) = 1: PARI does that according to [1], and I just verified that GNU MP does the same, so it is a reasonable assumption that this is the correct definition. I hope that no more cases are missing. — Emil J. 15:59, 4 March 2009 (UTC)[reply]

So kind of you to make that update. I appreciate it!—GraemeMcRae^talk 20:54, 4 March 2009 (UTC)[reply]

Properties/applications

A section on properties and/or applications of the Kronecker symbol would be appreciated. Which properties of the Legendre and Jacobi symbols does it share? -- Spireguy (talk) 17:31, 23 July 2010 (UTC)[reply]

Extend the Table of Values?

Since the Kronecker Symbol's arguments can be any integer, extending the table of values to include negative and zero arguments seems in order. Monolithic biavicide (talk) 14:38, 4 July 2019 (UTC)[reply]