#4940: dokchitser L-series at least for number fields claims a pole at zero,
though the zeta function has a zero there
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2.3
Component: number theory | Keywords:
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{{{
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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4940>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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