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On integer points in polygons. (English) Zbl 0779.11041
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the \(t\)-dilatation, \(t\to\infty\), of certain classes of irrational polygons the error terms are bounded as \(\ll\ln^ q t\) with some \(q>0\), or as \(\ll t^ \varepsilon\) with arbitrarily small \(\varepsilon>0\).

11P21 Lattice points in specified regions
11K38 Irregularities of distribution, discrepancy
11H06 Lattices and convex bodies (number-theoretic aspects)
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