Abstract
We prove the following conjecture of L. Moser: Any convex region of arean can be placed so as to cover ≧n+f(n) lattice points, wheref(n)→∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. S. Besicovitch, On the linear independence of fractionals powers of integers,J. London Math., Soc. 15 (1940), 3–6.
W. Blaschke,Kreis und Kugel, Leipzig: Gröschen 1916, New York: Chelsea 1949, Berlin: de Gruyter 1956.
W. Blaschke,Differentialgeometrie II, Affine Differentialgeometrie, Berlin: Springer 1923.
L. Fejes Tóth,Lagerungen in der Ebene, auf der Kugel und im Raum, Berlin: Springer 1953, 1972.
D. Koutroufiotis, On Blaschke's rolling theorem,Arch. Math.,23 (1972), 655–660.
L.Moser, Problem Section, in:Report of the Institute of the Theory of Numbers, Boulder, Colorado 1959.
W.Moser, Problem 12, in:Research problems in discrete geometry, Mimeograph notes, 1981.
W. M. Schmidt, Simultaneous approximation to algebraic numbers by rationals,Acta Math.,125 (1970), 189–201.
M. M. Skriganov, The spectrum of multidimensional operators with periodic coefficients (Russian),Funktsional. Anal. i. Prilozhen.,16 (1982) no. 4, 88–89.