ガロア第一論文及びその関連の資料スレ

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30: １３２人目の素数さん [sage] 2021/08/29(日) 18:37:00.62 ID:7niZQGlq

>>29
つづき

He employs the notation:
NRM=1.2.3...n,=number of different values the function can take,=size of each block;
so in the foregoing example, n=3,N=3!=6,R=3,M=2. Note that R?M=N, as developed above. Let's walk through another example to exemplify the theorem, with K(x1,x2,x3,x4,x5)=x1x2+x3x4+x5. We have n=5,N=5!=120 for this function. Since the largest prime less than or equal to n is now p=5, the theorem asserts that this or any other function cannot take a total of three or four values; ie, R≠3 and R≠4 for this function. Here are a few Ks with different values:

K1=a1a2+a3a4+a5K2=a1a4+a2a3+a5K3=a1a3+a2a4+a5.
Each one is associated with a block of functions, or substitutions if you will, giving the same value. K1, for example is associated with

K′1=a4a3+a1a2+a5,
where K1 and K′1 are identified respectively with the substitutions:

(1 2 3 4)
(1 2 3 4),

(1 2 3 4)
(4 3 1 2).

I'm leaving out the 5 even though they are substitutions on 5 letters, because the 5 is always unchanged for the first block (and the other two shown for that matter). It looks like there will be another four blocks like this, where each of a4,a3,a2,a1 plays the role of that last summand sitting at the end of K; that is, it looks like R=15 and therefore M=120/R=120/15=8. If so, K certainly satisfies the theorem.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1615510393/30

699: １３２人目の素数さん [] 2023/02/22(水) 16:24:56.62 ID:JXBpR2zJ

>>698
ありがとうございます

下記ですね
Hiroshi Inose氏 ね
京都大学の教授だったか

https://arxiv.org/pdf/1604.00738.pdf
Contemporary Mathematics
Volume 703, 2018
http://dx.doi.org/10.1090/conm/703/14134
Inose’s construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited
Abhinav Kumar and Masato Kuwata

References
[I1] Hiroshi Inose, On certain Kummer surfaces which can be realized as non-singular quartic surfaces in P3, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 3, 545?560.MR0429915
[I2] Hiroshi Inose, Defining equations of singular K3 surfaces and a notion of isogeny, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977),
Kinokuniya Book Store, 1978, 495?502. MR0578868
[SI] Tetsuji Shioda and Hiroshi Inose, On singular K3 surfaces, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 119?136. MR0441982

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はじめに
Global COE プロジェクト「数学のトップリーダーの育成」を開始してから，１年半が
経過した．国際交流などによるコア数学における研究者育成と多様な人材育成の２つの事業を行っている．
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Cohomologically trivial involutions of Enriques surfaces and Shioda-Inose correspondence, “Algebraic Geometry”,
Lorentz Center, Leiden, the Netherland, July 2, 2008 (International conference)
Homologically trivial involutions and Shioda-Inose correspondences for U+U(2), “Moduli and Discrete Groups”,
Res. Inst. Math. Sci., Kyoto Univ., June 10, 2009 (International conference)

http://rio2016.5ch.net/test/read.cgi/math/1615510393/699

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