Geodesic
Mean Oscillation Modulus and Number-Theoretic Grid Quadrature Formulas
Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 262-285

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For arbitrary Riemann integrable functions $f$ and irrational numbers $\theta \in (0,1)$, we obtain estimates of the error $R_n(f,\theta)$ of the quadrature formula $$ \int_{0}^{1}f(x)\,dx=\frac{1}{n}\sum_{k=1}^nf(\{k\theta\})- R_n(f,\theta) $$ in which $\{k\theta\}$ is the fractional part of the number $k\theta$.
Mots-clés : quadrature formula
Keywords: continued fraction, type of an irrational number, mean oscillation modulus. 
@article{MZM_2017_101_2_a10,
     author = {E. A. Sevast'yanov},
     title = {Mean {Oscillation} {Modulus} and {Number-Theoretic} {Grid} {Quadrature} {Formulas}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {262--285},
     publisher = {mathdoc},
     volume = {101},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a10/}
}
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E. A. Sevast'yanov. Mean Oscillation Modulus and Number-Theoretic Grid Quadrature Formulas. Matematičeskie zametki, Tome 101 (2017) no. 2, pp. 262-285. http://geodesic.mathdoc.fr/item/MZM_2017_101_2_a10/