Talk:Quadratic Gauss sum

Standard notation
I have looked in several books (Ireland and Rosen, Fröhlich and Taylor, et. al.) and have seen different notations for gauss sums, but not the one used here. Is this article really most representative of current standards in this area? (I am not an expert here, just interested - so comments from experts would be helpful!) Madmath789 21:44, 17 October 2006 (UTC)


 * I don't think there is an entirely standard notation. G(&chi;,&psi;) as at Gauss sum is pretty standard. This notation is OK, really. (I will claim to be a Gauss sum expert.) Charles Matthews 16:08, 18 October 2006 (UTC)


 * OK - I have also since found an example that agrees with the article (Apostol) - and I knew about your thesis being in this area :-) Madmath789 16:29, 18 October 2006 (UTC)

Derivation
Could you put up a derivation of the value of some easy Gauss sums, or at least a sketch of the proof? It seems that no one on the internet will even bother write a proof for this; I think that at least Wikipedia should be the source for it.

n = 0?
When evaluated at n = 0, the definition gives m, but the explicit formulae in Evaluation of Gauss sums do not agree.--80.136.153.37 08:39, 28 August 2007 (UTC)

Generalized Gauss sum
I was shocked at how incomprehensible this article was, in the large part due to the unsourced material on "Generalized Gauss sums" added by a single editor on June 14/15, 2008. While a relatively straightforward generalization, it is not common. For example, none of the three standard references in the article even define it! On the other hand, the classical quadratic Gauss sum mod p is neither presented in an easy to understand format, nor are its properties explored and explained. I even had a hard time locating its value, partly due to the unusual notation, and the question of the sign of the Gauss sum that, by his own admission, stumped Gauss himself for four years, is glossed over. I see two possible solutions:


 * Move the big section on "generalized Gauss sums" to a separate article "Generalized quadratic Gauss sum" (if the material can be sourced), preserving the edit history if possible (this may require administrative gimmicks).


 * Roll back to the version immediately preceding its addition and go from there.

Opinions? Arcfrk (talk) 02:12, 12 April 2010 (UTC)