[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 49 (1002ﾚｽ)
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542(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)11:50 ID:ZLSkSSTT(11/27) AAS
>>541
>※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.

そうか、この[Alien]っていうのが、重要な論文なんだね〜（＾＾
P4
[Alien]：
[Alien] S. Mochizuki, “The mathematics of mutually alien copies: From Gaussian integrals to Inter-universal
Teichmuller theory,” RIMS Preprint no. 1854, 169p. Jul. 2016, Eprint available on-line.
省15

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543: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)11:51 ID:ZLSkSSTT(12/27) AAS
>>542

つづき

・ the passage from planar cartesian to polar coordinates and the resulting splitting, or decoupling, into radial -i.e., in more abstract valuation-theoretic terminology, “value group” -and angular -i.e., in more abstract valuation-theoretic terminology, “unit group” -portions;
・ the straightforward evaluation of the radial portion by applying the quadraticity of the exponent of the Gaussian distribution;
・ the straightforward evaluation of the angular portion by considering the metric geometry of the group of units determined by a suitable version of the natural logarithm function.

[Here, the intended sense of the descriptive “alien” is that of its original Latin root, i.e., a
sense of abstract, tautological “otherness”.] After reviewing the classical computation
省5

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551(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)12:54 ID:ZLSkSSTT(16/27) AAS
>>542
>そうか、この[Alien]っていうのが、重要な論文なんだね〜（＾＾

"universe"の説明が詳しいね
以下抜粋する

（参考）
外部ﾘﾝｸ[pdf]:www.kurims.kyoto-u.ac.jp
[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory. PDF
省22

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