Opened 5 years ago

Last modified 2 months ago

#16586 new defect

K.zeta_function() unstable

Reported by: rws Owned by:
Priority: major Milestone: sage-6.4
Component: number fields Keywords: zeta, dokchitser, precision, lseries
Cc: jakobkroeker Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

This was reported by parzan in http://ask.sagemath.org/question/8418/zeta-function-gone-wild/

sage: K.<a> = NumberField(x^2-2)
sage: K.zeta_function()(7)
82.7603619399160
sage: K.zeta_function(prec=100)(7)
45333.379954778857657650185188
sage: K.zeta_function(prec=200)(7)
5.6555192254423051174292272646037247772094677139829119697339e8

See that excellent bug report for more aspects of the matter. Setting Component: to scripts because it seems to be a Dokchitser issue. See also #4940.

Change History (5)

comment:1 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:2 Changed 5 years ago by jdemeyer

  • Component changed from scripts to number fields

comment:3 Changed 3 years ago by jakobkroeker

  • Cc jakobkroeker added

comment:4 Changed 9 months ago by chapoton

This strange behaviour happens at odd integers >=7 only:

sage: Z = K.zeta_function(prec=100)
sage: Z(6.999999)
1.0078766853919870115865646404
sage: Z(7.000001)
1.0078766743798187778098456037
sage: Z(7.00000)
45333.379954778857657650185188

and the value depends strongly on the cutoff parameter

sage: Z = K.zeta_function(prec=100)
sage: gg = Z.gp()
sage: gg.eval('Lseries_5(7,1,0)')
'45333.379954778857657650185187902307852 + O(S)'
sage: gg.eval('Lseries_5(7,2,0)')
'38708792.158193667152030560998244936055 + O(S)'

This suggests something fishy in the dokchitser scripts..

Last edited 9 months ago by chapoton (previous) (diff)

comment:5 Changed 2 months ago by chapoton

This works now with the default algorithm. Still fails with Dokchitser's scripts:

sage: K.zeta_function(prec=100, algorithm="pari")(7)
1.0078766798859009530335817870
sage: K.zeta_function(prec=100, algorithm="gp")(7)
45333.379954778857657650185188
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