[過去ﾛｸﾞ] ガロア第一論文及びその関連の資料スレ (1002ﾚｽ)
上下前次1-新
抽出解除 必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞 あぼーん

---

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ

---

526(2): 2023/02/17(金)16:03 ID:PDN8ps3Q(1/4) AAS
>>489
>ちなみに、相互法則の重要性は単に整数論だけに閉じたものではないようで、ある種の
>相反性あるいは双対性を表しているものとして捉えられているもののようです。

関連追加
外部ﾘﾝｸ:en.wikipedia.org
Quadratic reciprocity
より
省30

---

529(1): 2023/02/17(金)16:32 ID:PDN8ps3Q(2/4) AAS
>>526 追加
>外部ﾘﾝｸ:en.wikipedia.org
>Quadratic reciprocity

＜関連追加引用＞
History and alternative statements
The theorem was formulated in many ways before its modern form: Euler and Legendre did not have Gauss's congruence notation, nor did Gauss have the Legendre symbol.
In this article p and q always refer to distinct positive odd primes, and x and y to unspecified integers.
省2

---

530(1): 2023/02/17(金)16:33 ID:PDN8ps3Q(3/4) AAS
>>529
つづき

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]

I confess that, as a student unaware of the history of the subject and unaware of the connection with cyclotomy, I did not find the law or its so-called elementary proofs appealing. I suppose, although I would not have (and could not have) expressed myself in this way that I saw it as little more than a mathematical curiosity, fit more for amateurs than for the attention of the serious mathematician that I then hoped to become. It was only in Hermann Weyl's book on the algebraic theory of numbers[28] that I appreciated it as anything more.
(引用終り)
省1

---

531(1): 2023/02/17(金)16:46 ID:PDN8ps3Q(4/4) AAS
>>501
>相互法則

ああ、これおっちゃんか！
お元気そうで、なによりです

相互法則関連は
>>526以下>>530までね

---

上下前次1-新書関写板覧索設栞歴

---

ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 0.036s