14 citations · 37 across the 12 of their papers we have counts for
7 papers · 1 filter
Irregularities of distribution and Fourier transforms of multi-dimensional convex bodies
Luca Brandolini, Leonardo Colzani, Giancarlo Travaglini
W. Schmidt, H. Montgomery, and J. Beck proved a result on irregularities of distribution with respect to -dimensional balls. In this paper, we extend their result to any -dim…
Convergence of multiple Fourier series and Pick's theorem
Luca Brandolini, Leonardo Colzani, Sinai Robins +1
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's t…
Mixed norms of the lattice point discrepancy
Leonardo Colzani, Bianca Gariboldi, Giacomo Gigante
We estimate some mixed norms of the discrepancy between the volume and the number of integer points in , a dilated by a factor and translated…
and Weak- estimates for the number of integer points in translated domains
Luca Brandolini, Leonardo Colzani, Giacomo Gigante +1
Revisiting and extending a recent result of M.Huxley, we estimate the and Weak- norms of the discrepancy be…
Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
Luca Brandolini, Leonardo Colzani, Giacomo Gigante +1
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 curva…
Quadrature rules and distribution of points on manifolds
Luca Brandolini, Christine Choirat, Leonardo Colzani +3
We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of th…