Mのジョルダン基底u、vを用て | |||||
u=(1,1)、v=(-1/2,0) | ∵γ={{1,1}、{0,1}} | ,γ^2={{1,2}、{0,1}} | |||
f=u+⒤v ∴⒤f=ーv+⒤u | |||||
∵⒤μ=√γ^2(if=ーv+iu)=ーv+⒤√γ^2‣u⋍1/2+⒤√(2m+1) | |||||
(リーマン)=⒤μ⋍1/2±11(文/11+s/11)⒤ | |||||
文/11 | s/11 | ∼ | s | 文/11+s/11 | ⋍√(2m+1) |
1.2849745454546 | 0.454545 | ∼ | 5 | 1.739520 | 1.73205 |
1.9110936363636 | 0.363636 | ∼ | 4 | 2.274730 | 2.23607 |
2.2737136363636 | 0.363636 | ∼ | 4 | 2.637350 | 2.64575 |
2.2737136363636 | 0.727273 | ∼ | 8 | 3.000986 | 3.00000 |
2.7658972727273 | 0.727273 | ∼ | 8 | 3.493170 | 3.31662 |
2.9940963636364 | 0.636364 | ∼ | 7 | 3.630460 | 3.60555 |
3.4169245454546 | 0.454545 | ∼ | 5 | 3.871470 | 3.87298 |
3.7198827272727 | 0.272727 | ∼ | 3 | 3.992610 | 4.12311 |
3.9388245454546 | 0.454545 | ∼ | 5 | 4.393370 | 4.35890 |
3.9388245454546 | 0.454545 | ∼ | 5 | 4.393370 | 4.58258 |
4.3641045454546 | 0.454545 | ∼ | 5 | 4.818650 | 4.79583 |
4.5248936363636 | 0.363636 | ∼ | 4 | 4.888530 | 5.00000 |
4.8154545454546 | 0.454545 | ∼ | 5 | 5.270000 | 5.19615 |
5.1314545454546 | 0.454545 | ∼ | 5 | 5.586000 | 5.38516 |
5.3951818181818 | 0.181818 | ∼ | 2 | 5.577000 | 5.56776 |
5.5300909090909 | 0.636364 | ∼ | 7 | 6.166455 | 5.74456 |
5.5300909090909 | 0.090909 | ∼ | 1 | 5.621000 | 5.91608 |
5.9192727272727 | 0.272727 | ∼ | 3 | 6.192000 | 6.08276 |
5.9192727272727 | 0.272727 | ∼ | 3 | 6.192000 | 6.24500 |
6.8909090909091 | 0.909091 | ∼ | 10 | 7.800000 | 7.68115 |
6.8909090909091 | 0.909091 | ∼ | 10 | 7.800000 | 7.81025 |
∵⒤M=⒤√γ^2(f=u+Iv)=1/2+⒤√(2m+1) | ||||||
(リーマン)=1/2±11(s/11+文/11)⒤⋍√γ^2‣u | ||||||
Mのジョルダン基底u、vを用いて | ||||||
u=(1,1)、y=(-1/2,0) | ||||||
f=u+⒤v∴⒤f=ーv+⒤u | ||||||
∵γ^2=F[1,1,0]F[1,1,0]=F[1,2,0] | ||||||
γ1^2 | = | 1,1 | 1,1 | = | 1,2 | |
0,1 | 0,1 | 0,1 | ||||
∴F[1,2,0]u=γ^2n‣u⋍{2n+1,1}t | ||||||
γ^2‣u | = | 1,2 | 1 | = | 3 | |
0,1 | 1 | 1 | ||||
γ^4‣u | = | 1,2 | 3 | = | 5 | |
0,1 | 1 | 1 | ||||
γ^2‣v | = | 1,2 | ー1/2 | = | ー1/2 | ∴-γ^2‣v=1/2 |
0,1 | 0 | 0 | ||||
M^n‣u | = | 1,2 | 2n-1 | = | 2n+1 | |
0,1 | 1 | 1 | ||||
(リーマン)=1/2±11(文ブン/11+s/11)⒤⋍√γ^2‣u |
Mのジョルダン基底u、vを用いて | ||||||
u=(1,1)、y=(-1/2,0) | ||||||
f=u+⒤v ∴⒤f=ーv+⒤u | ||||||
∵γ^2=F[1,1,0]F[1,1,0]=F[1,2,0] | ||||||
γ1^2 | = | 1,1 | 1,1 | = | 1,2 | |
0,1 | 0,1 | 0,1 | ||||
∴F[1,2,0]u=γ^2n‣u⋍{2n+1,1}t | ||||||
γ^2‣u | = | 1,2 | 1 | = | 3 | |
0,1 | 1 | 1 | ||||
γ^4‣u | = | 1,2 | 3 | = | 5 | |
0,1 | 1 | 1 | ||||
γ^2‣v | = | 1,2 | ー1/2 | = | ー1/2 | ∴-γ^2‣v=1/2 |
0,1 | 0 | 0 | ||||
M^n‣u | = | 1,2 | 2n-1 | = | 2n+1 | |
0,1 | 1 | 1 | ||||
(リーマン)=1/2±11(文ブン/11+s/11)⒤⋍√γ^2‣u |
Φ(z)はモジュラー、Δ=1,c=0(mod32、32の倍数) | |||||
∵Φ^2=F[1,1,0]F[1,1,0]=F[1,2,0] | |||||
γ1^2 | = | 1,1 | 1,1 | = | 1,2 |
0,1 | 0,1 | 0,1 | |||
F[1,2,0]u=Φ^2n‣u⋍{2n+1,1} | |||||
Φ^2‣u | = | 1,2 | 1 | = | 3 |
0,1 | 1 | 1 | |||
M^2‣u | = | 1,2 | 3 | = | 5 |
0,1 | 1 | 1 | |||
M^3‣u | = | 1,2 | 5 | = | 7 |
0,1 | 1 | 1 | |||
M^n‣u | = | 1,2 | 2n-1 | = | 2n+1 |
0,1 | 1 | 1 | |||
(リーマン)=1/2±11(文/11+s/11)⒤⋍√Φ^2‣u | |||||
s/11 | ∼ | s | 文/11+s/11 | ‣ | √(2m+1) |
0.454545 | ∼ | 5 | 1.739520 | ‣ | 1.73205 |
0.363636 | ∼ | 4 | 2.274730 | ‣ | 2.23607 |
0.363636 | ∼ | 4 | 2.637350 | ‣ | 2.64575 |
0.727273 | ∼ | 8 | 3.000986 | ‣ | 3.00000 |
0.727273 | ∼ | 8 | 3.493170 | ‣ | 3.31662 |
0.636364 | ∼ | 7 | 3.630460 | ‣ | 3.60555 |
0.454545 | ∼ | 5 | 3.871470 | ‣ | 3.87298 |
0.272727 | ∼ | 3 | 3.992610 | ‣ | 4.12311 |
0.454545 | ∼ | 5 | 4.393370 | ‣ | 4.35890 |
0.454545 | ∼ | 5 | 4.393370 | ‣ | 4.58258 |
0.454545 | ∼ | 5 | 4.818650 | ‣ | 4.79583 |
0.363636 | ∼ | 4 | 4.888530 | ‣ | 5.00000 |
0.454545 | ∼ | 5 | 5.270000 | ‣ | 5.19615 |
0.454545 | ∼ | 5 | 5.586000 | ‣ | 5.38516 |
0.181818 | ∼ | 2 | 5.577000 | ‣ | 5.56776 |
0.636364 | ∼ | 7 | 6.166455 | ‣ | 5.74456 |
0.090909 | ∼ | 1 | 5.621000 | ‣ | 5.91608 |
0.272727 | ∼ | 3 | 6.192000 | ‣ | 6.08276 |
0.272727 | ∼ | 3 | 6.192000 | ‣ | 6.24500 |
0.909091 | ∼ | 10 | 7.800000 | ‣ | 7.68115 |
0.909091 | ∼ | 10 | 7.800000 | ‣ | 7.81025 |
∴F[1,2,0]u=M^n‣u⋍{2n+1,1}t | |||||
M‣u | = | 1,2 | 1 | = | 3 |
0,1 | 1 | 1 | |||
M^2‣u | = | 1,2 | 3 | = | 5 |
0,1 | 1 | 1 | |||
M^3‣u | = | 1,2 | 5 | = | 7 |
0,1 | 1 | 1 | |||
M^n‣u | = | 1,2 | 2n-1 | = | 2n+1 |
0,1 | 1 | 1 |