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math.NT2013★ 3 cited
Estimates of the Discrepancy Function in Exponential Orlicz Spaces
Gagik Amirkhanyan, Dmitriy Bilyk, Michael T Lacey
We prove that in all dimensions n at least 3, for every integer N there exists a distribution of points of cardinality , for which the associated discrepancy function D_N satis…
math.NT2013★ 3 cited
Dichotomy Results for the L1 Norm of the Discrepancy Function
Gagik Amirkhanyan, Dmitriy Bilyk, Michael T Lacey
It is a well-known conjecture in the theory of irregularities of distribution that the L1 norm of the discrepancy function of an N-point set satisfies the same asymptotic lower bou…