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math.CA2023
Single radius spherical cap discrepancy via gegenbadly approximable numbers
Dmitriy Bilyk, Michelle Mastrianni, Stefan Steinerberger
A celebrated result of Beck shows that for any set of points on there always exists a spherical cap such that number of points in the ca…
math.CA2022
Lower bounds for the directional discrepancy with respect to an interval of rotations
Dmitriy Bilyk, Michelle Mastrianni
We show that the lower bound for the optimal directional discrepancy with respect to the class of rectangles in rotated in a restricted interval of directions $[-θ,…