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Jun 1, 2011 at 3:23 vote accept isildur
May 31, 2011 at 22:22 answer added paul garrett timeline score: 16
May 25, 2011 at 0:00 history edited Qfwfq CC BY-SA 3.0
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May 24, 2011 at 23:57 history edited GH from MO
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May 24, 2011 at 22:27 answer added GH from MO timeline score: 10
May 24, 2011 at 22:22 comment added Kevin Buzzard Someone will probably come along with a proper answer later on, but here's something one could think about until then: imagine the case of $GL(1)$ over the rationals. If $K$ is all of $\hat{\mathbf{Z}}$ and you demand invariance, rather than finiteness, then (a) and (b) together just give you an arbitrary ($C^\infty$) function on the positive reals. The growth condition is just "doesn't grow too fast" but if you don't put any more conditions then you have a space which is perhaps far too big to be of arithmetic interest.
May 24, 2011 at 21:05 history asked isildur CC BY-SA 3.0