Timeline for Number fields with same zeta function?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 30, 2021 at 4:05 | comment | added | Yuan Yang | @AlexB. Thanks very much！ | |
| May 29, 2021 at 23:56 | comment | added | Alex B. | @YuanYang See this paper of Perlis, for example: sciencedirect.com/science/article/pii/0022314X77900701#. The basic point is that the zeta function determines the set of split primes, which determines the Galois closure. | |
| May 29, 2021 at 11:19 | comment | added | Yuan Yang | Dear Alex，can you elaborate more about why arithmetically equivalent fields share a same Galois closure? | |
| Nov 10, 2011 at 21:21 | vote | accept | pki | ||
| Nov 9, 2011 at 20:58 | comment | added | Ben Webster♦ | Qiaochu: Yes, the construction is exactly the same. Look in this paper of Sunada: jstor.org/stable/1971195?seq=1 | |
| Nov 9, 2011 at 15:01 | comment | added | Alex B. | Dear Qiaochu, yes, I think that's correct, although I don't know the details. | |
| Nov 9, 2011 at 14:04 | comment | added | Qiaochu Yuan | I understand the idea in the first paragraph can also be used to write down examples of non-isometric compact Riemannian manifolds which are isospectral (which I think is equivalent to having the same Selberg zeta function...?). | |
| Nov 9, 2011 at 1:38 | history | edited | Alex B. | CC BY-SA 3.0 |
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| Nov 9, 2011 at 1:31 | history | edited | Alex B. | CC BY-SA 3.0 |
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| Nov 9, 2011 at 1:16 | comment | added | KConrad | To make the first paragraph even more concrete, the condition imposed on $H$ and $H'$ is equivalent to saying for every conjugacy class $C$ in $G$ that $H \cap C$ and $H' \cap C$ have the same size. | |
| Nov 9, 2011 at 0:40 | history | edited | Alex B. | CC BY-SA 3.0 |
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| Nov 9, 2011 at 0:26 | history | answered | Alex B. | CC BY-SA 3.0 |