Abstract
AbstractWe study the speed of convergence in the numerical integration with Weyl sums over Kronecker sequences in the torus, $$\begin{aligned} \dfrac{1}{N}\sum _{n=1}^{N}f\left( x+n\alpha \right) -\int _{\mathbb {T}^{d} }f(y)dy. \end{aligned}$$
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Funder
Università degli Studi di Milano - Bicocca
Publisher
Springer Science and Business Media LLC
Reference22 articles.
1. Bayart, F., Buczolich, Z., Heurteaux, Y.: Fast and slow points of Birkhoff sums. Ergodic Theory Dyn. Syst. 40(12), 3236–3256 (2020)
2. Beck, J.: Probabilistic Diophantine approximation I. Kronecker sequences. Ann. Math. 140, 449–502 (1994)
3. Beck, J.: From Khinchin’s conjecture on strong uniformity to superuniform motions. Mathematika 61, 591–707 (2015)
4. Brandolini, L., Choirat, C., Colzani, L., Gigante, G., Seri, R., Travaglini, G.: Quadrature rules and distribution of points on manifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13(4), 889–923 (2014)
5. Dick, J., Pillichshammer, F.: Periodic functions with bounded remainder. Arch. Math. 87(6), 554–563 (2006)
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