零点p=1/2+ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)φのｎ乗和

5次元重力→４次元＋電磁場＋p(ディラトン)スカラー場
11次元重力→10次元＋電磁場のような場＋φ^n+(-1/φ)^ｎ
竹内『次元の秘密』p129よりφ^n+(-1/φ)^ｎ(n乗和)は、
∴φ^1+(-1/φ)^1＝１
φ^2+(-1/φ)^2＝３
φ^3+(-1/φ)^3＝４
φ^4+(-1/φ)^4＝７
虚根の部分を①ｱｲﾋﾗｰ(1/11)で有理(連分数)化、②ｶﾞｳｽ(1/1.6)で連分数③ｾﾙﾊﾞ―ぐ(5)
mod5 mod16 mod11
零点p=1/2+ ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)
※a/b=q+1/b/r(連分数)
文献値 文/1.1(ｱｲﾋﾗｰ) 1/11/r *-1/11/r /1.6(ｶﾞｳｽ) -s/9 /5(ｾﾙﾊﾞ)
14.13472 12.84974545 1/11/20 12.3952 0.688622222 2/9 0.4664
21.02203 19.11093636 4/11 18.7473 1.041516667 6/9 0.374850667
25.01085 22.73713636 4/11 22.3735 1.242972222 2/9 1.02075
30.42487 27.65897273 3/11 26.9317 1.496205555 5/9 0.940650005
32.93506 29.94096364 4/11 29.3046 1.628033333 3/9 1.294700003
37.58617 34.16924545 1/11/20 33.7147 1.873038889 8/9 0.984150089
40.91871 37.19882727 3/11 36.9261 2.05145 0.41029
43.32707 39.38824545 1/11/20 38.9337 2.162983334 3/9 1.829650004
48.00515 43.64104545 1/11/20 43.1865 2.39925 0.47985
49.77383 45.24893636 4/11 44.8853 2.493627778 7/9 1.715850778
52.97 48.15454545 1/11/20 47.7 2.65 0.53
56.446 51.31454545 1/11/20 50.86 2.825555556 5/9 2.270000006
59.347 53.95181818 1/11/20 53.77 2.987222222 2/9 2.765
60.831 55.30090909 1/11/20 55.21 3.067222222 2/9 2.845
65.112 59.19272727 3/11 58.92 3.273333333 3/9 2.940000003
76.8 69.81818182 9/11 69 3.833333333 3/9 3.500000003

*

零点p=1/2+ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)

　　　　　mod5 　　　mod16　　　mod11
零点p=1/2+ ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)
※a/b=q+1/b/r(連分数)
文献値 文/1.1(ｱｲﾋﾗｰ) 1/11/r *-1/11/r /1.6(ｶﾞｳｽ) s/9 /5(ｾﾙﾊﾞ)
14.13472 12.84974545 1/11/20 12.3952 0.688622222 2/9 0.4664
21.02203 19.11093636 4/11 18.7473 1.041516667 6/9
25.01085 22.73713636 4/11 22.3735 1.242972222 2/9 1.02075
30.42487 27.65897273 3/11 26.9317 1.496205555 5/9 0.940650005
32.93506 29.94096364 4/11 29.3046 1.628033333 3/9 1.294700003
37.58617 34.16924545 1/11/20 33.7147 1.873038889 8/9
40.91871 37.19882727 3/11 36.9261 2.05145 0.41029
43.32707 39.38824545 1/11/20 38.9337 2.162983334 3/9
48.00515 43.64104545 1/11/20 43.1865 2.39925 0.47985
49.77383 45.24893636 4/11 44.8853 2.493627778 7/9
52.97 48.15454545 1/11/20 47.7 2.65 0.53
56.446 51.31454545 1/11/20 50.86 2.825555556 5/9
59.347 53.95181818 1/11/20 53.77 2.987222222 2/9 2.765
60.831 55.30090909 1/11/20 55.21 3.067222222 2/9 2.845
65.112 59.19272727 3/11 58.92 3.273333333 3/9 2.940000003
76.8 69.81818182 9/11 69 3.833333333 3/9 3.500000003

⋆

零点p=1/2+ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)

零点p=1/2+ ｾﾙﾊﾞ-ｸﾞ(abba)+ｶﾞｳｽ(s/9)+ｱｲﾋﾗｰ(1/11/r)
※a/b=q+1/b/r(連分数)
文献値 文/1.1(ｱｲﾋﾗｰ) 1/11/r *-1/11/r /1.6(ｶﾞｳｽ) s/9 /5(ｾﾙﾊﾞ)
14.13472 12.84974545 1/11/20 12.3952 0.688622222 2/9 0.4664
21.02203 19.11093636 4/11 18.7473 1.041516667 6/9
25.01085 22.73713636 4/11 22.3735 1.242972222 2/9 1.02075
30.42487 27.65897273 3/11 26.9317 1.496205555 5/9 0.940650005
32.93506 29.94096364 4/11 29.3046 1.628033333 3/9 1.294700003
37.58617 34.16924545 1/11/20 33.7147 1.873038889 8/9
40.91871 37.19882727 3/11 36.9261 2.05145 0.41029
43.32707 39.38824545 1/11/20 38.9337 2.162983334 3/9
48.00515 43.64104545 1/11/20 43.1865 2.39925 0.47985
49.77383 45.24893636 4/11 44.8853 2.493627778 7/9
52.97 48.15454545 1/11/20 47.7 2.65 0.53
56.446 51.31454545 1/11/20 50.86 2.825555556 5/9
59.347 53.95181818 1/11/20 53.77 2.987222222 2/9 2.765
60.831 55.30090909 1/11/20 55.21 3.067222222 2/9 2.845
65.112 59.19272727 3/11 58.92 3.273333333 3/9 2.940000003
76.8 69.81818182 9/11 69 3.833333333 3/9 3.500000003

⋆

ラグランジアンにφ^4などがる(φ^4理論)

a(p)三τ(p)mod11(アイヒラ―の定理)連分数(有理数)
1/11=0.0909090909
1/1.1=0.90909090909 零点p=1/2+ 16Mz+g(1/11/r)
1/0.11=9,0909090909 ※a/b=q+1/b/r(連分数)ラグランジアンにφ^4などがる
文献値 /16 円周率Mz 文/1.1(有理数) 1/b/r r φ^n+(-1/φ)^n
14.13472 0.88342 16b4(0.874) 12.84974545 1/11/20 20 2+4乗和
21.02203 1.313876875 8ω 19.11093636 4/11 1/4 3乗和
25.01085 1.563178125 8π 22.73713636 4/11 1/4 3乗和
30.42487 1.901554375 16b2(1.90) 27.65897273 3/11 1/3 2乗和
32.93506 2.05844125 4ωπ 29.94096364 4/11 1/4 3乗和
37.58617 2.349135625 8ωB4 34.16924545 1/11/20 20 2+4乗和
40.91871 2.557419375 16ω 37.19882727 3/11 1/3 2乗和
43.32707 2.707941875 8πB4 39.38824545 1/11/20 20 2+4乗和
48.00515 3.000321875 πB2 43.64104545 1/11/20 20 2+4乗和
49.77383 3.110864375 16π 45.24893636 4/11 1/4 2乗和
52.97 3.310625 16π 48.15454545 1/11/20 20 2+4乗和
56.446 3.527875 8ω^2 51.31454545 1/11/20 20 2+4乗和
59.347 3.7091875 16φω 53.95181818 1/11/20 20 2+4乗和
60.831 3.8019375 24ω 55.30090909 1/11/20 20 2+4乗和
65.112 4.0695 8ωπ 59.19272727 3/11 1/3 2乗和
76.8 4.8 69.81818182 9/11 1/9

⋆

零点p=1/2+16Mz+g(1/11/r)

a(p)三τ(p)mod11(アイヒラ―の定理)連分数(有理数)
1/11=0.0909090909
1/1.1=0.90909090909 零点p=1/2+ 16Mz+g(1/11/r)
1/0.11=9,0909090909 ※a/b=q+1/b/r(連分数)
文献値 /16 円周率Mz 文/1.1(有理数) 1/b/r r
14.13472 0.88342 16b4(0.874) 12.84974545 1/11/20 20
21.02203 1.313876875 8ω 19.11093636 4/11 1/4
25.01085 1.563178125 8π 22.73713636 4/11 1/4
30.42487 1.901554375 16b2(1.90) 27.65897273 3/11 1/3
32.93506 2.05844125 4ωπ 29.94096364 4/11 1/4
37.58617 2.349135625 8ωB4 34.16924545 1/11/20 20
40.91871 2.557419375 16ω 37.19882727 3/11 1/3
43.32707 2.707941875 8πB4 39.38824545 1/11/20 20
48.00515 3.000321875 πB2 43.64104545 1/11/20 20
49.77383 3.110864375 16π 45.24893636 4/11 1/4
52.97 3.310625 16π 48.15454545 1/11/20 20
56.446 3.527875 8ω^2 51.31454545 1/11/20 20
59.347 3.7091875 16φω 53.95181818 1/11/20 20
60.831 3.8019375 24ω 55.30090909 1/11/20 20
65.112 4.0695 8ωπ 59.19272727 3/11 1/3
76.8 4.8 69.81818182 9/11 1/9

⋆