AbstractIf C is a strictly convex plane curve of length l, it has been known for a long time that the number of integer lattice points on C is O(l23) and the exponent is best possible. In this paper, it is shown that the exponent can be decreased by imposing suitable smoothness conditions on C; in particular, if C has a continuous third derivative with a sensible bound, the best possible value of the exponent lies between 35 and 13 inclusive
A convex plane set S is discretized by first mapping the centre of S to a point (u, v), preserving o...
It is known that convex polygonal lines on Z 2 with the endpoints fixed at 0 = (0, 0) and n = (n1, n...
13 pages, 2 figuresAn asymptotic formula is presented for the number of planar lattice convex polygo...
AbstractIf C is a strictly convex plane curve of length l, it has been known for a long time that th...
Let C be a smooth convex closed plane curve. The C -ovals C(R,u,v) are formed by expanding by a f...
AbstractOn lattice points in the Euclidean planeFor a large parameter T, let D(T) denote a domain in...
We solve a randomized version of the following open question: is there a strictly convex, bounded cu...
AbstractLeo Moser conjectured that given ε > 0 there is a δ > 0 such that any closed convex plane cu...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
AbstractLeo Moser conjectured that given ε > 0 there is a δ > 0 such that any closed convex plane cu...
Abstract. We consider planar curved strictly convex domains with no or very weak smoothness assumpti...
Let D be a compact convex set in R2, containing 0 as an interior point, having a smooth boundary cur...
A convex plane set S is discretized by first mapping the centre of S to a point (u, v), preserving o...
A lattice point in the plane is a point with integer coordinates. A lattice polygon is a polygon who...
A convex plane set S is discretized by first mapping the centre of S to a point (u, v), preserving o...
It is known that convex polygonal lines on Z 2 with the endpoints fixed at 0 = (0, 0) and n = (n1, n...
13 pages, 2 figuresAn asymptotic formula is presented for the number of planar lattice convex polygo...
AbstractIf C is a strictly convex plane curve of length l, it has been known for a long time that th...
Let C be a smooth convex closed plane curve. The C -ovals C(R,u,v) are formed by expanding by a f...
AbstractOn lattice points in the Euclidean planeFor a large parameter T, let D(T) denote a domain in...
We solve a randomized version of the following open question: is there a strictly convex, bounded cu...
AbstractLeo Moser conjectured that given ε > 0 there is a δ > 0 such that any closed convex plane cu...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
When a strictly convex plane set S moves by translation, the set J of points of the integer lattice ...
AbstractLeo Moser conjectured that given ε > 0 there is a δ > 0 such that any closed convex plane cu...
Abstract. We consider planar curved strictly convex domains with no or very weak smoothness assumpti...
Let D be a compact convex set in R2, containing 0 as an interior point, having a smooth boundary cur...
A convex plane set S is discretized by first mapping the centre of S to a point (u, v), preserving o...
A lattice point in the plane is a point with integer coordinates. A lattice polygon is a polygon who...
A convex plane set S is discretized by first mapping the centre of S to a point (u, v), preserving o...
It is known that convex polygonal lines on Z 2 with the endpoints fixed at 0 = (0, 0) and n = (n1, n...
13 pages, 2 figuresAn asymptotic formula is presented for the number of planar lattice convex polygo...
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