Andreas Holmstrom
Reputation
3,154
Next privilege 5,000 Rep.
Approve tag wiki edits
 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 awarded Good Answer Nov 8 awarded Nice Question Oct 14 awarded Yearling Sep 2 awarded Popular Question Apr 8 awarded Good Question Mar 19 awarded Popular Question Feb 16 asked Geometric vs combinatorial motives over Spec Z Feb 5 awarded Enthusiast Nov 13 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! Nov 12 awarded Popular Question Nov 10 awarded Nice Question Nov 10 asked Big list of repositories of mathematical preprints and postprints Nov 2 awarded Notable Question Oct 14 awarded Yearling