不変量ｊ⋍1728(一定)

α⋍1/2+δ⒤	β⋍1/2-δ⒤とおく
(x-α)(x-β)⋍	x＾2-(α+β)x+αβ
∵α+β⋍1､αβ⋍1/4+δ^2
⋍x＾2-x+1/4+δ^2
⋍(x-1/2)^2+δ^2			s=1+ℓとおくとﾙｼﾞｬﾝﾄﾞﾙ
①ｵﾒｶﾞωとﾙｼﾞｬﾝﾄﾞﾙ
		ω^2+ω+1	⋍0
楕円曲	y^2⋍	x^3+Px+Q	x(x＾2+δ^2)+Q
不変量	ｊ⋍	2^83＾3P^3	/（	4P^3+27Q^2）				Q⋍0のときの不変量ｊ
	δ^2		-δ				文献値	2^83＾3P^3	/	4P^3+27Q^2）	ｊ(一定)
∴11√	3	19.05256	5	⋍	14.05256	~	14.13472	6912	/	4	1728
∴11√	5	24.59675	4	⋍	21.09675	~	21.02203	55296	/	32	1728
∴11√	7	29.10326	4	⋍	25.10326	~	25.01085	186624	/	108	1728
∴11√	9	33	3	⋍	30.5	~	30.42487	442368	/	256	1728
∴11√	11	36.48287	4	⋍	32.98287	~	32.93506	864000	/	500	1728
∴11√	13	39.66106	2	⋍	37.66106	~	37.58617	1492992	/	864	1728
∴11√	15	42.60282	2	⋍	40.60282	~	40.91871	2370816	/	1372	1728
∴11√	17	45.35416	2	⋍	43.35416	~	43.32707	3538944	/	2048	1728
∴11√	19	47.94789	0	⋍	47.94789	~	48.00515	5038848	/	2916	1728
∴11√	21	50.40833	1	⋍	49.40833	~	49.77383	6912000	/	4000	1728
∴11√	23	52.75415	0	⋍	52.75415	~	52.97	9199872	/	5324	1728
∴11√	25	55	0	⋍	55	~	56.446	11943936	/	6912	1728
∴11√	27	57.15768	1	⋍	56.65768	~	56.446	15185664	/	8788	1728
∴11√	29	59.23681	0	⋍	59.23681	~	59.347	18966528	/	10976	1728
∴11√	31	61.24541	1	⋍	60.74541	~	60.831	23328000	/	13500	1728
∴11√	33	63.19019	0	⋍	63.19019	~	65.112	28311552	/	16384	1728

O,t^2-3t+1⋍(t-φ^2)(t-1/φ^2

⓪	三角関数の合成関数がﾌｯｸの法則を満たす.
①	{1/φ^2,1/φ,φ,φ^2}が4次元を示すこと｡
	ｱﾚｸｻﾝﾀﾞｰ
C	t^2-t+1		(t-ω)(t+ω)
O	t^2-3t+1		(t-φ^2)(t-1/φ^2)
…	2t^2-5t+2		(t-0.5)(tｰ2)
	n	)	φ^n	∓	1/φ^n
	1	)	1.618	ｰ	0.618	⋍	1
	2	)	2.618	+	0.381924	⋍	3
	3	)	4.235801	ｰ	0.145866	⋍	4
	4	)	17.943573	+	0.021277	⋍	18

①gμν⋍η-δ⋍11√(2k+1)-δ

①gμν⋍η-δ⋍11√(2k+1)-δ
	η			δ			文献値
11√	3	19.053	-	5	⋍	14.05256	14.13472
11√	5	24.597	-	3.5	⋍	21.09675	21.02203
11√	7	29.103	-	4	⋍	25.10326	25.01085
11√	9	33	-	2.5	⋍	30.5	30.42487
11√	11	36.483	-	3.5	⋍	32.98287	32.93506
11√	13	39.661	-	2	⋍	37.66106	37.58617
11√	15	42.603	-	2	⋍	40.60282	40.91871
11√	17	45.354	-	2	⋍	43.35416	43.32707
11√	19	47.948	-	0	⋍	47.94789	48.00515
11√	21	50.408	-	1	⋍	49.40833	49.77383
11√	23	52.754	-	0	⋍	52.75415	52.97
11√	25	55	-	0	⋍	55	56.446
11√	27	57.158	-	0.5	⋍	56.65768	56.446
11√	29	59.237	-	0	⋍	59.23681	59.347
11√	31	61.245	-	0.5	⋍	60.74541	60.831
11√	33	63.19	-	0	⋍	63.19019	65.112

(x-1/2)^2+δ^2

α⋍1/2＋δ⒤､	β⋍1/2-δ⒤とおく
(x-α)(x-β)⋍	x＾2-(α+β)x+αβ
∵α+β⋍1､αβ⋍1/4+δ^2
⋍x＾2-x+1/4+δ^2
⋍(x-1/2)^2+δ^2
(s)ｰ2-4-6ｰ8ｰ10…
(1-s)3,5,7,9.11,…
ｓと1-sを入れ替えても成立,s=1+ℓとおくと
∴s(1-s)=ｰℓ(ℓ+1)=ｰα(α+1)ﾙｼﾞｬﾝﾝﾄﾞﾙの関係式使った
x(x+1)+121[(2k+1.25)-δ]⋍0		⋍19.05-5⋍14.05
x＾2+ｘ+3.25-δ⋍0　∴x⋍(-0.5)±[11√3-δ]⒤
p⋍(１/2)±11⒤[√(1-s)-(q/11)]
文献値	文/11	(	s	)	+s/11	⋍√2k+1	⋍2k+1
14.13472	1.28497454545455	(	5	)	0.45454545454546	1.73952	3.026
21.02203	1.91109363636364	(	4	)	0.36363636363636	2.27473	5.174
25.01085	2.27371363636364	(	4	)	0.36363636363636	2.63735	6.956
30.42487	2.76589727272727	(	6	)	0.54545454545455	3.31135	10.965
32.93506	2.99409636363636	(	7	)	0.63636363636364	3.63046	13.180
37.58617	3.41692454545455	(	5	)	0.45454545454546	3.87147	14.988
40.91871	3.71988272727273	(	5	)	0.45454545454546	4.17443	17.426
43.32707	3.93882454545455	(	5	)	0.45454545454546	4.39337	19.302
48.00515	4.36410454545455	(	5	)	0.45454545454546	4.81865	23.219
49.77383	4.52489363636364	(	4	)	0.36363636363636	4.88853	23.898
52.97	4.81545454545455	(	5	)	0.45454545454546	5.27000	27.773
56.446	5.13145454545455	(	5	)	0.45454545454546	5.58600	31.203
59.347	5.39518181818182	(	2	)	0.18181818181818	5.57700	31.103
60.831	5.53009090909091	(	1	)	0.09090909090909	5.62100	31.596
65.112	5.91927272727273	(	3	)	0.27272727272727	6.19200	38.341
75.8	6.89090909090909	(	10	)	0.90909090909091	7.80000	60.840

x＾2+ｘ+3.25-δ⋍0 x⋍(-0.5)±11[√3-δ]⒤

(s)ｰ2-4-6ｰ8ｰ10…
(1-s)3,5,7,9.11,…
ｓと1-sを入れ替えても成立,s=1+ℓとおく
∴s(1-s)=ｰℓ(ℓ+1)=ｰα(α+1)ﾙｼﾞｬﾝﾝﾄﾞﾙの関係式使った
x(x+1)+121[(2k+1.25)-δ]⋍0		⋍19.05-5⋍14.05
x＾2+ｘ+3.25-δ⋍0　x⋍(-0.5)±11[√3-δ]⒤
p⋍(１/2)±11⒤[√(1-s)-(q/11)]
文献値	文/11	(	s	)	+s/11	⋍√2k+1	⋍2k+1
14.13472	1.28497454545455	(	5	)	0.45454545454546	1.73952	3.026
21.02203	1.91109363636364	(	4	)	0.36363636363636	2.27473	5.174
25.01085	2.27371363636364	(	4	)	0.36363636363636	2.63735	6.956
30.42487	2.76589727272727	(	6	)	0.54545454545455	3.31135	10.965
32.93506	2.99409636363636	(	7	)	0.63636363636364	3.63046	13.180
37.58617	3.41692454545455	(	5	)	0.45454545454546	3.87147	14.988
40.91871	3.71988272727273	(	5	)	0.45454545454546	4.17443	17.426
43.32707	3.93882454545455	(	5	)	0.45454545454546	4.39337	19.302
48.00515	4.36410454545455	(	5	)	0.45454545454546	4.81865	23.219
49.77383	4.52489363636364	(	4	)	0.36363636363636	4.88853	23.898
52.97	4.81545454545455	(	5	)	0.45454545454546	5.27000	27.773
56.446	5.13145454545455	(	5	)	0.45454545454546	5.58600	31.203
59.347	5.39518181818182	(	2	)	0.18181818181818	5.57700	31.103
60.831	5.53009090909091	(	1	)	0.09090909090909	5.62100	31.596
65.112	5.91927272727273	(	3	)	0.27272727272727	6.19200	38.341