Opened 11 years ago

Last modified 5 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 11 years ago by mabshoff

  • Milestone changed from sage-3.2.3 to sage-3.4

comment:2 Changed 11 years ago by robertwb

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 6 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:4 Changed 6 years ago by chapoton

  • Keywords dokchitser added
  • Report Upstream set to N/A

comment:5 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:6 Changed 6 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:7 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4
Note: See TracTickets for help on using tickets.