Timeline for What is an automorphic representation of CM type ?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2012 at 12:32 | comment | added | Emerton | Dear unknown, The distribution in the CM case has been known since Hecke, and is much simpler. (The relevant $L$-functions reduce to abelian, or Hecke, $L$-functions for the CM extension, whose analytic properties were established by Hecke.) Regards, | |
| Jun 26, 2012 at 6:27 | comment | added | user4245 | David Hansen: Thanks ! It looks like a characterization rather than a definition. | |
| Jun 26, 2012 at 3:56 | comment | added | David Hansen | A "pure" representation-theory definition: a $GL_2$ automorphic representation $\pi$ is of CM type if there is a quadratic idele class character $\eta$ such that $\pi \simeq \pi \otimes \eta$. | |
| Jun 26, 2012 at 3:41 | comment | added | user4245 | @Emerton: Thank you ! Has the distribution law in the CM case been already known in general ? | |
| Jun 26, 2012 at 3:34 | vote | accept | user4245 | ||
| Jun 26, 2012 at 3:09 | comment | added | Emerton | Dear unknown, The distribution law for Hecke eigenvalues is different in the CM and non-CM cases (e.g. because the Mumford--Tate groups are quite different in the two cases). This is probably discussed in various expository articles about Sato--Tate, such as the one by Mazur. Regards, Matthew | |
| Jun 25, 2012 at 17:35 | answer | added | Joël | timeline score: 5 | |
| Jun 25, 2012 at 16:56 | history | asked | user4245 | CC BY-SA 3.0 |