Geodesic
A lower bound for the error of a formula for approximate summation in the class $E_{s,p}(C)$
Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 371-375 Cet article a éte moissonné depuis la source Math-Net.Ru

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The error of a formula for approximate summation in the class $E_{s,p}(C)$ over an arbitrary mesh containing p base-points is shown to be not less than $C_1\ln^sp/p$. This estimate has the same order as the error of the optimal parallelepiped mesh in this class. 
@article{MZM_1977_21_3_a8,
     author = {I. F. Sharygin},
     title = {A~lower bound for the error of a~formula for approximate summation in the class $E_{s,p}(C)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {371--375},
     year = {1977},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a8/}
}
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I. F. Sharygin. A lower bound for the error of a formula for approximate summation in the class $E_{s,p}(C)$. Matematičeskie zametki, Tome 21 (1977) no. 3, pp. 371-375. http://geodesic.mathdoc.fr/item/MZM_1977_21_3_a8/