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Dynamics seminar: Nadav Yesha (Kings College): Pair correlation for quadratic polynomials mod 1 | Einstein Institute of Mathematics

Dynamics seminar: Nadav Yesha (Kings College): Pair correlation for quadratic polynomials mod 1

Date: 
Tue, 21/03/201714:00-15:00
It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. We provide explicit Diophantine conditions on the coefficients of degree 2 polynomials under which the limit of an averaged pair correlation density is consistent with the Poisson distribution, using a recent effective Ratner equidistribution result on the space of affine lattices due to Strömbergsson. This is joint work with Jens Marklof.