Talk:Proofs of quadratic reciprocity

From Wikipedia, the free encyclopedia

These things need to be done:

  1. Clean up, wikify and check what I've written.
  2. Finish the bits of that proof that I haven't written yet (in particular the calculation of the quadratic subfield of the cyclotomic field via gauss sums, or whatever method).
  3. Add explanation of how to get the "supplementary theorems" in the same spirit as the proof I have partially written.
  4. Last but CERTAINLY NOT LEAST, write up a proof that doesn't use all that algebraic number theory!!! i.e. one that is accessible -- yes such proofs do exist!

Dmharvey Image:User_dmharvey_sig.png Talk 03:10, 6 November 2005 (UTC)

Two elementary proofs you might like are Hammick 2001: http://www3.telus.net/ldh/math/qrl.html and Zolotarev 1872: http://planetmath.org/encyclopedia/ZolotarevsLemma.html

[edit] eisenstein's proof

I've added half of eisenstein's proof. The other half ("eisenstein's lemma") still needs to be written.

  • Yes Oleg, I know you think section stubs are ugly, but I'm tired now, and I promise I will make the stub notice disappear in the next few days :-)
done now Dmharvey 11:56, 14 April 2006 (UTC)
  • I read about this proof at http://math.nmsu.edu/~history/eisenstein/eisenstein.html, but it would be nice to have a primary reference for it.
  • I don't know whether "Eisenstein's lemma" is a nonstandard name for this result, perhaps coined in the above-mentioned article, or whether it is is standard.

Dmharvey 02:42, 14 April 2006 (UTC)

I think Eisenstein's proof is

Geometrischer Beweis des Fundamentaltheorems für die quadratischen Reste, J. Reine Angew. Math. 28 (1844), 246-248; Math. Werke I, 164-166

but I haven't checked. The textbook proof is a slight variation of E's original.

LDH 01:48, 22 April 2007 (UTC)