Abstract
The exact order of the remainder term is determined in the formula for the number of lattice points in the region α 1∥ u 1 + b 1∥ + α 2∥ u 2 + b 2∥ + … + α r ∥ u r + b r ∥ ≤ x in dependence on the arithmetical properties of the coefficients α 1, α 2,…, α r .
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