Opened 8 years ago

# K.zeta_function() unstable

Reported by: Owned by: rws major sage-6.4 number fields zeta, dokchitser, precision, lseries jakobkroeker N/A

### 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.

### comment:1 Changed 8 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:2 Changed 8 years ago by jdemeyer

• Component changed from scripts to number fields

### comment:4 Changed 3 years 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 3 years ago by chapoton (previous) (diff)

### comment:5 Changed 3 years 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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