Abstract
LetG 2 (R) denote the number of lattice points (x, y) (i. e. points of the plane with integer coordinates) in the domainx a+y a ≤R,x≥0,y≥0 (with weight 1/2 ifxy=0) and letV 2 (a)R 2/a be the area of this region. Then for 0<a<1/3 it is known [2] thatG 2 (R)−V 2 (a)R 2/a ∼K(a)R (1/a)−1. Combining a method due toBleicher andKnopp [1] with a result proved elsewhere [4], [5] by the author it is shown here thatG 2 (R)=V 2 (a)R 2/a +Ω(R (1/a)−1) for any fixed rational numbera with 1/3<a<1/2.
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Literatur
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Nowak, WG. Eine Ω-Abschätzung zu einem zweidimensionalen Gitterpunktproblem. Monatshefte für Mathematik 94, 143–147 (1982). https://doi.org/10.1007/BF01301932
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DOI: https://doi.org/10.1007/BF01301932