Lattice Points in Planar Convex Domains

2004 ◽  
Vol 143 (2) ◽  
pp. 145-162 ◽  
Author(s):  
Ekkehard Kr�tzel
Keyword(s):  
Lattice Points ◽  
Convex Domains ◽  
Planar Convex

scholarly journals On the maximal circumradius of a planar convex set containing one lattice point

1995 ◽  
Vol 52 (1) ◽  
pp. 137-151 ◽  
Author(s):  
Poh W. Awyong ◽  
Paul R. Scott
Keyword(s):  
Lattice Point ◽  
Convex Set ◽  
Compact Convex ◽  
Lattice Points ◽  
Compact Convex Set ◽  
Planar Convex

We obtain a result about the maximal circumradius of a planar compact convex set having circumcentre O and containing no non-zero lattice points in its interior. In addition, we show that under certain conditions, the set with maximal circumradius is a triangle with an edge containing two lattice points.

Geometry of the gauss map and lattice points in convex domains

Mathematika ◽  
2001 ◽  
Vol 48 (1-2) ◽  
pp. 107-117 ◽  
Author(s):  
L. Brandolini ◽  
L. Colzani ◽  
A. Iosevich ◽  
A. Podkorytov ◽  
G. Travaglini
Keyword(s):  
Gauss Map ◽  
Lattice Points ◽  
Convex Domains

Geometry of the Gauss Map and Lattice Points in Convex Domains

2014 ◽  
pp. 161-171
Author(s):  
Alex Iosevich ◽  
Elijah Liflyand
Keyword(s):  
Gauss Map ◽  
Lattice Points ◽  
Convex Domains

scholarly journals Random fluctuations of convex domains and lattice points

1999 ◽  
Vol 127 (10) ◽  
pp. 2981-2985
Author(s):  
Alex Iosevich ◽  
Kimberly K. J. Kinateder
Keyword(s):  
Lattice Points ◽  
Convex Domains ◽  
Random Fluctuations

scholarly journals Circumradius-diameter and width-inradius relations for lattice constrained convex sets

1999 ◽  
Vol 59 (1) ◽  
pp. 147-152 ◽  
Author(s):  
Poh Wah Awyong ◽  
Paul R. Scott
Keyword(s):  
Lattice Point ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Integer Lattice ◽  
Lattice Points ◽  
Compact Convex Set ◽  
Planar Convex ◽  
Rectangular Lattices

Let K be a planar, compact, convex set with circumradius R, diameter d, width w and inradius r, and containing no points of the integer lattice. We generalise inequalities concerning the ‘dual’ quantities (2R − d) and (w − 2r) to rectangular lattices. We then use these results to obtain corresponding inequalities for a planar convex set with two interior lattice points. Finally, we conjecture corresponding results for sets containing one interior lattice point.

scholarly journals On the area of planar convex sets containing many lattice points

1987 ◽  
Vol 35 (3) ◽  
pp. 441-454
Author(s):  
P. R. Scott
Keyword(s):  
Large Class ◽  
Convex Sets ◽  
Convex Set ◽  
Lattice Points ◽  
Symmetric Convex ◽  
Classical Theorem ◽  
Planar Convex

A classical theorem of van der Corput gives a bound for the volume of a symmetric convex set in terms of the number of lattice points it contains. This theorem is here generalized and extended for a large class of non-symmetric sets in the plane.

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