Inter-universal geometry と ABC予想 (応援スレ) 52

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 52 (1002ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除ﾚｽ栞

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

52: １３２人目の素数さん [] 2021/02/20(土) 21:07:22.66 ID:Z8PgJDTw

>>45
>The following research topics emphasize this seminal idea: (a) Galois covers, G-torsors and their parametrizing families, (b) motivic Galois representations, (c) anabelian towers of fundamental groups.
>Striking advances have recently shed new light on the whole topic:
>(c) in Anabelian Geometry: the successful introduction of methods from étale homotopy theory
>(Schmidt-Stix) and from motivic A1-homotopy theory for moduli stacks of curves (Collas), the import
>of operads (Fresse-Horel) which echo the Galois techniques of Pop and ,
>the construction of arithmetic operads for Hurwitz moduli spaces (Westerland-Wickelgren).

”Striking advances have recently shed new light on the whole topic:”
ですね

”Hoshi-Mochizuki-Minamide”は、該当しそうなのは下記二つ
（>>5より）
http://www.kurims.kyoto-u.ac.jp/~yuichiro/papers.html
星裕一郎の論文
(抜粋)
１）Explicit estimates in inter-universal Teichmüller theory (with Shinichi Mochizuki, Ivan Fesenko, Arata Minamide, and Wojciech Porowski) RIMS Preprint 1933 (November 2020): (PDF).
　http://www.kurims.kyoto-u.ac.jp/~yuichiro/rims1933.pdf
２）Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups (with Arata Minamide and Shinichi Mochizuki) RIMS Preprint 1870 (March 2017): 修正版: (PDF).
　http://www.kurims.kyoto-u.ac.jp/~yuichiro/rims1870revised.pdf
（引用終り）

ここで、”Striking advances have recently shed new light on the whole topic:”に該当するのは、”November 2020”の１）”Explicit estimates in inter-universal Teichmüller theory”ですね
”March 2017”は、ちょっと古いですね
たぶんね

http://rio2016.5ch.net/test/read.cgi/math/1613784152/52

302: １３２人目の素数さん [] 2021/02/27(土) 12:51:48.66 ID:f+hU2HEr

>>301
>the Legendre form
>ここらが重要キーワードですね

参考
https://en.wikipedia.org/wiki/Legendre_form
Legendre form

Contents
1 Definition
2 Numerical evaluation
3 References

The respective complete elliptic integrals are obtained by setting the amplitude, Φ, the upper limit of the integrals, to π/2.

The Legendre form of an elliptic curve is given by
y2 = x(x-1)(x-λ)

Numerical evaluation
The classic method of evaluation is by means of Landen's transformations. Descending Landen transformation decreases the modulus   k k towards zero, while increasing the amplitude Φ. Conversely, ascending transformation increases the modulus towards unity, while decreasing the amplitude. In either limit of k, zero or one, the integral is readily evaluated.

Most modern authors recommend evaluation in terms of the Carlson symmetric forms, for which there exist efficient, robust and relatively simple algorithms. This approach has been adopted by Boost C++ Libraries, GNU Scientific Library and Numerical Recipes.[3]

http://rio2016.5ch.net/test/read.cgi/math/1613784152/302

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 0.032s