The Limiting Curve of Jarnik's Polygons

Details The Limiting Curve of Jarnik's Polygons The Limiting Curve of Jarnik's Polygons

2002-06-17

arxiv.org/abs/math/0206168v1

Mathematics

Number Theory

16 pages; 11 figures

Scientific paper

In 1925, Jarnik 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 Jarnik's construction.

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