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Título: | Close Lattice Points on Circles |
Autor: | Cilleruelo, Javier; Granville, Andrew | Fecha de publicación: | dic-2009 | Editor: | University of Toronto | Citación: | Canadian Journal of Mathematics 61(6): 1214-1238 (2009) | Resumen: | We classify the sets of four lattice points that all lie on a short arc of a circle that has its center at the origin; specifically on arcs of length tR1/3 on a circle of radius R, for any given t > 0. In particular we prove that any arc of length (40 + 40/3 √10)1/3 R1/3 on a circle of radius R, with R > √65, contains at most three lattice points, whereas we give an explicit infinite family of 4-tuples of lattice points, (v1,n,v2,n,v3,n,v4,n), each of which lies on an arc of length (40 + 40/3√10)1/3 R1/3n + o(1) on a circle of radius Rn. | Descripción: | 25 páginas.-- MSC Classifications: 11N36. | Versión del editor: | http://dx.doi.org/10.4153/CJM-2009-057-2 | URI: | http://hdl.handle.net/10261/31054 | DOI: | 10.4153/CJM-2009-057-2 | ISSN: | 0008-414X |
Aparece en las colecciones: | (ICMAT) Artículos |
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closelattice.pdf | 223,9 kB | Adobe PDF | Visualizar/Abrir |
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