24/01/18 15:57:51.71 Q8ip59pc.net
>>782
>ガウスの円分論の一つの到達点は、円分論に
>よる平方剰余の相互法則の証明。
>平方剰余の相互法則
>URLﾘﾝｸ(ja.wikipedia.org)
>これは数論なのであって、現代において
>ガロア理論が重視される理由も、この関連。
１）ja.wikipediaを見たら、en.wikipediaをチェックするくせをつけるのがいいぞ
そうすると、”Connection with cyclotomic fields”が見つかる
２）「ガロア理論が重視される理由も、この関連」は
どういう意味か多義だが（言い訳の余地はある）、外れの可能性大だな
(参考)
URLﾘﾝｸ(en.wikipedia.org)
Quadratic reciprocity
Connection with cyclotomic fields
The early proofs of quadratic reciprocity are relatively unilluminating. The situation changed when Gauss used Gauss sums to show that quadratic fields are subfields of cyclotomic fields, and implicitly deduced quadratic reciprocity from a reciprocity theorem for cyclotomic fields. His proof was cast in modern form by later algebraic number theorists. This proof served as a template for class field theory, which can be viewed as a vast generalization of quadratic reciprocity.
Robert Langlands formulated the Langlands program, which gives a conjectural vast generalization of class field theory. He wrote:[27]
略
It was only in Hermann Weyl's book on the algebraic theory of numbers[28] that I appreciated it as anything more.