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Feb
28
awarded  Nice Question
Feb
28
comment Can the Dedekind zeta function distinguish between real and imaginary quadratic number fields?
But maybe two values on either side of a negative even integer would work? If I compute say $\zeta_K(1.9)*\zeta_K(2.1)$, this should be strictly positive if K is real and strictly negative if K is imaginary. And in principle I can use interval arithmetic to know for sure which case we're in. But if I really want to do this, is it not a problem that I do not know the form of the functional equation?
Feb
28
comment Can the Dedekind zeta function distinguish between real and imaginary quadratic number fields?
@KConrad, thanks for the answer, but even if I can compute values of $\zeta_K$, I cannot know for sure that the value at 0 is precisely 0 and not, say $2^{-500}$. Or do we have some additional knowledge about zeta functions of quadratic number fields which implies that if the value is smaller than some bound $b$, then it really is equal to zero?
Feb
28
comment Can the Dedekind zeta function distinguish between real and imaginary quadratic number fields?
Thanks Noam! So if I have an upper bound B on the discriminant, how do I actually determine whether the field is real or imaginary? And is it possible to express (in terms of B) how many a_n (or how many Euler factors) I need?
Feb
28
asked Can the Dedekind zeta function distinguish between real and imaginary quadratic number fields?
Dec
28
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asked Geometric vs combinatorial motives over Spec Z
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asked How to check whether a scheme of finite type over Spec Z is regular or not
Nov
13
comment Big list of repositories of mathematical preprints and postprints
I guess this kind of directory is precisely what I was looking for. But unfortunately all the links are dead!
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Nov
10
asked Big list of repositories of mathematical preprints and postprints
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