Opened 12 years ago
Last modified 6 years ago
#4940 new defect
dokchitser L-series at least for number fields claims a pole at zero, though the zeta function has a zero there
Reported by: | was | Owned by: | was |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | number theory | Keywords: | dokchitser |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
sage: K.<a> = NumberField(x^2-2) sage: z = K.zeta_function() sage: z(0) Traceback (most recent call last): ... ArithmeticError: ### user error: L*(s) has a pole at s=0 sage: z(0.0000001) -4.40686861437826e-8
Notice that there is in fact a zero at s=0, not a pole as the ArithmeticError? claims.
In fact, it's a theorem that there is a zero at s=0 of order the unit rank of the number field.
Change History (7)
comment:1 Changed 12 years ago by
- Milestone changed from sage-3.2.3 to sage-3.4
comment:2 Changed 12 years ago by
comment:3 Changed 7 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:4 Changed 7 years ago by
- Keywords dokchitser added
- Report Upstream set to N/A
comment:5 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:6 Changed 6 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:7 Changed 6 years ago by
- Milestone changed from sage-6.3 to sage-6.4
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The function
L*(s) = sqrt(8)^s/pi^s * gamma(s/2)^2
does have a pole at s=0, even though L(s) doesn't. That being said, it shouldn't raise this error.I have made some progress on the re-implementation of dokchitser the last couple of days.