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{\Large Department of Mathematics, BGU}

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{\Huge BGU Probability and Ergodic Theory  (PET) seminar}\\[0.2\baselineskip]

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\textbf{On} \emph{Thursday, November 28, 2019}
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\textbf{At} \emph{11:10 -- 12:00}
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\textbf{In} \emph{-101}

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{\large\scshape Manuel Luethi 
  %
  (Tel-Aviv University)
}
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will talk about
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{\Large\bfseries Effective equidistribution of primitive rational points along long horocycle orbits and disjointness to Kloosterman sums\par}
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\textsc{Abstract:}
An observation by Jens Marklof shows that the primitive
rational points of a fixed denominator along the periodic unipotent
orbit of volume equal to the square of the denominator equidistribute
inside a proper submanifold of the modular surface. This concentration
as well as the equidistribution are intimately related to classical
questions of number theoretic origin. We discuss the distribution of the
primitive rational points along periodic orbits of intermediate size. In
this case, we can show joint equidistribution with polynomial rate in
the modular surface and in the torus. We also deduce simultaneous
equidistribution of primitive rational points in the modular surface and
of modular hyperbolas in the two-torus under certain congruence
conditions. This is joint work with M. Einsiedler and N. Shah.








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