Timeline for Number fields with same zeta function?
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| Dec 30, 2011 at 16:55 | comment | added | Alex B. | Hi Andreas, greetings from Korea! Just a small note: your point 1. follows immediately from my first paragraph together with Keith's characterisation in his comment to my answer. Indeed, let $H$ and $H'$ correspond to the two fields. Since the fields are Galois over $\mathbb{Q}$, $H$ and $H'$ are normal in $G$. But then they are both unions of conjugacy classes of $G$. If in addition you know that the intersections with all conjugacy classes have the same size, then it immediately follows that $H=H'$. | |
| Dec 30, 2011 at 13:47 | history | answered | Andreas Holmstrom | CC BY-SA 3.0 |