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Asymptotics of Weighted Lattice Point Counts Inside Dilating Polygons

  • Marina NechayevaEmail author
  • Burton Randol
Chapter

Summary

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.

Keywords

Lattice point asymptotics Polygons 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.LaGuardia Community CollegeLong Island CityUSA

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