Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus

We produce explicit low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a convex domain with positive curvature in R^2. The proof depends on simultaneous diophantine approximation and a general version of the Erdos-Turan inequality.Comment: 14 pages, 2 figure

LpL^{p} and Weak-LpL^{p} estimates for the number of integer points in translated domains

Revisiting and extending a recent result of M.Huxley, we estimate the $L^{p}\left( \mathbb{T}^{d}\right)$ and Weak-$L^{p}\left( \mathbb{T}^{d}\right)$ norms of the discrepancy between the volume and the number of integer points in translated domains

Transference for hypergroups

A transference theorem for convolution operators is proved for certain families of one-dimensional hypergroups