Timeline for The meaning of $L_{\chi}^2(G(\mathbb Q) \backslash G(\mathbb A)^1)$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2022 at 16:04 | comment | added | Tian An | I meant that one should always work with $L^2(G(\mathbb Q)\backslash G(\mathbb A)^1)$ or something like $L^2(Z(\mathbb A)G(\mathbb Q)\backslash G(\mathbb A))$ for the reasons you mentioned. | |
| Sep 8, 2022 at 21:37 | comment | added | D_S | So $L^2(G(\mathbb Q) \backslash G(\mathbb A))$ is really as the notation suggests, and consists of all measureable functions on $G(\mathbb A)$ which are $G(\mathbb Q)$-invariant and satisfy $\int\limits_{G(\mathbb Q) \backslash G(\mathbb A)} |f(g)|^2 dg < \infty$? This seems strange, since $G(\mathbb Q) \backslash G(\mathbb A)$ doesn't usually have finite volume. | |
| Sep 8, 2022 at 3:20 | history | answered | Tian An | CC BY-SA 4.0 |