Talk:Hilbert's twelfth problem

from the article
This does not seem to be particularly relevant for the Jugendtraum itself, so let's park it here for the time being. Arcfrk 00:35, 12 April 2007 (UTC)


 * Robert Langlands wrote an important report (Ein Märchen) in relation to automorphic representation theory and extension of the Jugendtraum. The presumable reason for his lapse into German can be explained: Märchen is fairy tale, and his conclusion in respect of extensions came down on the negative side, at least from his viewpoint or Langlands philosophy. The main thrust, on this view, of the higher-dimensional theory is to get control of Shimura varieties, their special points (CM-points), and automorphic L-functions. Evaluation of transcendental functions at given points to create specific algebraic numbers is not dealt with..


 * Well, it matters in a sense. Charles Matthews 15:42, 12 April 2007 (UTC)

The quote from Kronecker's letter to Dedekind …
… in English reads: It is about my favourite childhood dream, namely to prove that the Abel’s equations with square roots of rational numbers are just as exhausted by the transformation equations of elliptical functions with singular modules, as the integer Abel’s equations are by the circle division equations.

Is this worth sharing in the article? --yoyo (talk) 02:06, 30 May 2021 (UTC)

Difficult to understand
I find the writing in this article unnecessarily difficult to understand.

For instance, shortly after it is explained that Hilbert used the phrase "elliptic functions" in an ambiguous way, the 'article' uses the same phrase without any disambiguation: "More seriously, while values of elliptic modular functions generate the Hilbert class field, for more general abelian extensions one also needs to use values of elliptic functions."

A bit later, the article uses the phrase "singular moduli" with no explanation or link.

I hope someone knowledgeable about this subject can make this article a lot clearer.