Talk:Stark–Heegner theorem

PID != UFD

Being a PID is not equivalent to being a UFD—a priori, the claim in the paper only proves one direction of the theorem. If in this context UFD implies PID, that should be noted. Tesseran 00:11, 6 January 2006 (UTC)[reply]

The ring of integers of a number field is a Dedekind domain, and a DD is a UFD iff it is a PID. Algebraist

Author

Admiral Harold Rainsford Stark is not the author of Stark(-Heegner) theorem.

The author is Harold M. Stark. One can find a list of his papers at

http://www.mtholyoke.edu/~aschwart/stark/papers.html

Applies to

The statement about factorization of ideals applies to the ring of integers of the number field, not the number field itself, as asserted in the article. --Coolpapabell 22:41, 15 October 2006 (UTC)[reply]

What gap in Heegner's proof???

The article says:

"This result was first conjectured by Gauss. It was essentially proven by Kurt Heegner in 1952, but Heegner's proof had some minor gaps and the theorem was not accepted until Harold Stark gave a complete proof in 1967, which Stark showed was actually equivalent to Heegner's. Heegner "died before anyone really understood what he had done". Stark formally filled in the gap in Heegner's proof in 1969."

1. The result wasn't merely "conjectured" by Gauss; he proved these nine imaginary quadratic rings of integers were in fact unique factorization rings, and conjectured they were the only imaginary quadratic rings of integers with this property.

2. What gaps in Heegner's proof? As the article states -- Heegner's proof was not fully understood before Stark's re-proof using essentially the same methods. But my understanding is that Heegner's proof was then seen not to have had gaps in it.

3. And then in the last quoted sentence above, the "gaps" in Heegner's proof suddenly become just one gap. How about zero?Daqu (talk) 07:06, 8 January 2010 (UTC)[reply]