108 citations · 814 across the 70 of their papers we have counts for
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The distribution of spacings between fractional parts of lacunary sequences
Zeev Rudnick, Alexandru Zaharescu
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed…
On quantum ergodicity for linear maps of the torus
P. Kurlberg, Z. Rudnick
We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (``cat maps''). We show that there is a density one sequence of integers so that as N tends…
Quantum unique ergodicity for parabolic maps
Jens Marklof, Zeev Rudnick
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of qua…
Hecke theory and equidistribution for the quantization of linear maps of the torus
P. Kurlberg, Z. Rudnick
We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus ("cat map"). For some values of Planck's constant, the spectrum of the q…