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Pardon the wild question, but

Are there any known connections between Kazhdan's property (T) and number theory, or number theoretic consequences of property (T)?

Edit: To clarify, I'd like to know if there are consequences of property (T) in modern number theory that are significant to number theorists, and in what way are they significant (I'm not a number theorist, and so mostly am looking for enrichment on how thing fit together!)

Thanks, in advance, for any thoughts or references!

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    Inasmuch as Kazhdan's property is related to expander graphs, a connection with number theory is given via Ramanujan graphs and cryptography.2012-08-18

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At least as a place-holder answer: in the last few years several people have proven subconvexity bounds on $L$-functions by using Ratner's Lemma from the ergodic theory of $SL_2(\mathbb R)$ and such... which has some relation to property $(T)$, in my limited understanding of these things. E.g., Michel-Venkatesh' paper on subconvexity for $GL(2)$ is an example of such a viewpoint.

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    This is interesting. Thanks!2012-08-18
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Property $T$ for a real group implies vanishing of the $1$st Betti number for its arithmetic subgroups. Do you consider this number theory? (I do.)

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    Thanks! Do $y$ou have a reference where I can learn more about such things?2012-08-18