Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons

  • Marina NechayevaEmail author
  • Burton Randol


We study the family of normalized discrete measures induced on the unit circle by radially projecting onto the circle the integral lattice points contained in dilations of a fixed polygon satisfying certain algebraic properties. We examine the asymptotic effect of such measures on a function f on S 1 by weighting the lattice points and their projections by a homogeneous extension of f to R 2. We then derive an almost everywhere result for almost all rotations of the polygon.


Lattice point asymptotics Polygons 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.LaGuardia Community CollegeLong Island CityUSA

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