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The limiting curve of Jarník's polygons

Author(s): Greg Martin
Journal: Trans. Amer. Math. Soc. 355 (2003), 4865-4880.
MSC (2000): Primary 52C05; Secondary 11H06
Posted: July 28, 2003
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Abstract: In 1925, Jarník defined a sequence of convex polygons for use in constructing curves containing many lattice points relative to their curvatures. Properly scaled, these polygons converge to a certain limiting curve. In this paper we identify this limiting curve precisely, showing that it consists piecewise of arcs of parabolas, and we discuss the analogous problem for sequences of polygons arising from generalizations of Jarník's construction.

References:

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3.: V. Jarník, Über die Gitterpunkte auf konvexen Kurven, Math. Zeitschrift 24 (1925), 500-518.
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