Abstract
We investigate the equidistribution of Hecke eigenforms for PSL 2 ( Z ) ${\hbox{PSL}_2({\mathbb {Z}})}$ on sets that are shrinking toward the cusp. We show that at scales finer than the Planck scale they do not equidistribute while at scales more coarse than the Planck scale they equidistribute on a full density subsequence of eigenforms. On a suitable set of test functions we compute the variance showing an interesting transition behavior at half the Planck scale.
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