Timeline for Definition of cusp form in $L^2$ and convergence over $N_{\mathbb Q} \backslash N_{\mathbb A}$
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| Oct 27, 2020 at 23:38 | comment | added | paul garrett | And, yes, $L^1_{loc}$'s can work, too, but I think these are just an approximation to spaces of distributions... I feel that spaces of distributions are more robust. Tastes vary. :) | |
| Oct 27, 2020 at 23:36 | comment | added | paul garrett | Yes, for example ... surely not the only way... the way that I myself finally feel secure/safe with "the constant term map" is as a map from $L^2$ (or even a bigger space) to distributions on $U_k\backslash G_{\mathbb A}$ (or whatever). After that, yes, we can (as in my book) prove continuity in a finer topology on the target space, but it's not obvious, etc. Mercifully, everything works fine, in the usual quasi-miraculous idiot-proof-ness of most of mathematics, so that, in particular, obliviousness of these issues seems not to easily lead to disaster. :) | |
| Oct 27, 2020 at 22:48 | history | answered | paul garrett | CC BY-SA 4.0 |