5 papers · 1 filter
Poisson statistics via the Chinese remainder theorem
A. Granville, P. Kurlberg
We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem.…
On the distribution of matrix elements for the quantum cat map
P. Kurlberg, Z. Rudnick
For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phas…
On a character sum problem of H. Cohn
Par Kurlberg
Let be a complex valued function on a finite field such that , , and for . Cohn asked if it follows that is a nontrivial mult…
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…
The distribution of spacings between quadratic residues, II
P. Kurlberg
We study the distribution of spacings between squares modulo q as the number of prime divisors of q tends to infinity. In an earlier paper Kurlberg and Rudnick proved that the spac…