Number Theory Seminar
Speaker: Ezra Waxman
Title: Lattice Points in Thin Sectors
Abstract: On the circle of radius R centred at the origin, consider a ``thin'' sector about the fixed line x=ay with edges given by the lines y=(a+/-\eps)x where \eps =\eps_R -> 0 as R -> infinity. We discuss an asymptotic count for S_a(\eps,R), the number of integer lattice points lying in such a sector, and moreover present results concerning the variance of such lattice points across sectors.
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