Revision history [back]
 | 1 | initial version |
Do not use Dokchister implementation, but always the pari implementation.
sage: K = NumberField(x**2 + x + 1,'a')
sage: Qbis = NumberField(x-1,'y')
sage: KL = K.zeta_function()
sage: QL = Q.zeta_function()
sage: KL(-1)
0.000000000000000
sage: QL(-1)
-0.0833333333333333
so the quotient will be zero. You can use taylor series as follows
sage: KL.taylor_series(-1,4)
0.000000000000000 - 0.0269221622682875*z - 0.0573141973539488*z^2 - 0.0443122899350116*z^3 + O(z^4)
We also have L functions for Dirichlet characters.
sage: D = DirichletGroup(4)
sage: chi = D.gen(0)
sage: chi.lfunction()
PARI L-function associated to Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1
| | 2 | No.2 Revision |
Do not use Dokchister implementation, but always the pari implementation.
sage: K = NumberField(x**2 + x + 1,'a')
sage: Qbis Q = NumberField(x-1,'y') # using QQ should work, this is a workaround
sage: KL = K.zeta_function()
sage: QL = Q.zeta_function()
sage: KL(-1)
0.000000000000000
sage: QL(-1)
-0.0833333333333333
so the quotient will be zero. You can use taylor series as follows
sage: KL.taylor_series(-1,4)
0.000000000000000 - 0.0269221622682875*z - 0.0573141973539488*z^2 - 0.0443122899350116*z^3 + O(z^4)
We also have L functions for Dirichlet characters.
sage: D = DirichletGroup(4)
sage: chi = D.gen(0)
sage: chi.lfunction()
PARI L-function associated to Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1
| | 3 | No.3 Revision |
Do not use Dokchister implementation, but always the pari implementation.
sage: K = NumberField(x**2 + x + 1,'a')
sage: Q = NumberField(x-1,'y') # using QQ should work, this is a workaround
sage: KL = K.zeta_function()
sage: QL = Q.zeta_function()
sage: KL(-1)
0.000000000000000
sage: QL(-1)
-0.0833333333333333
so the quotient will be zero. You can use taylor series as follows
sage: KL.taylor_series(-1,4)
0.000000000000000 - 0.0269221622682875*z - 0.0573141973539488*z^2 - 0.0443122899350116*z^3 + O(z^4)
We also have L functions for Dirichlet characters.
sage: D = DirichletGroup(4)
sage: chi = D.gen(0)
sage: chi.lfunction()
PARI L-function associated to Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1
| | 4 | No.4 Revision |
Do not use Dokchister Dokchitser implementation, but always the pari implementation.
sage: K = NumberField(x**2 + x + 1,'a')
sage: Q = NumberField(x-1,'y') # using QQ should work, this is a workaround
sage: KL = K.zeta_function()
sage: QL = Q.zeta_function()
sage: KL(-1)
0.000000000000000
sage: QL(-1)
-0.0833333333333333
so the quotient will be zero. You can use taylor series as follows
sage: KL.taylor_series(-1,4)
0.000000000000000 - 0.0269221622682875*z - 0.0573141973539488*z^2 - 0.0443122899350116*z^3 + O(z^4)
We also have L functions for Dirichlet characters.
sage: D = DirichletGroup(4)
sage: chi = D.gen(0)
sage: chi.lfunction()
PARI L-function associated to Dirichlet character modulo 4 of conductor 4 mapping 3 |--> -1
