Opened 14 years ago

Last modified 8 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: William Stein Owned by: William Stein
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:

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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 14 years ago by Michael Abshoff

Milestone: sage-3.2.3sage-3.4

comment:2 Changed 14 years ago by Robert Bradshaw

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.

comment:3 Changed 9 years ago by Jeroen Demeyer

Milestone: sage-5.11sage-5.12

comment:4 Changed 9 years ago by Frédéric Chapoton

Keywords: dokchitser added
Report Upstream: N/A

comment:5 Changed 9 years ago by For batch modifications

Milestone: sage-6.1sage-6.2

comment:6 Changed 8 years ago by For batch modifications

Milestone: sage-6.2sage-6.3

comment:7 Changed 8 years ago by For batch modifications

Milestone: sage-6.3sage-6.4
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