The Limiting Curve of Jarnik's Polygons

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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.
16 pages; 11 figures

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Number Theory, 52C05 (11H06)

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http://salesiana.dossiersoluciones.com/handle/123456789/64322

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206168
 http://arxiv.org/abs/math/0206168

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arXiv