A Lower Bound for the Volume of Strictly Convex Bodies with Many Boundary Lattice Points

@inproceedings{Andrews2010ALB,
  title={A Lower Bound for the Volume of Strictly Convex Bodies with Many Boundary Lattice Points},
  author={George E. Andrews},
  year={2010}
}
In a recent paper it was shown that if a strictly convex body C in n-dimensional space contains N noncoplanar lattice points (i.e., points with integer coordinates) on its boundary, then S(C)>fc(n)JV("+1)/" where SiC) denotes the surface area of C and kin) > 0 is a constant depending only on n [1]. If F(C) denotes the volume of C and ViC)^c'in)[SiC)JK"-1) where c'(«) > 0 is a constant depending only on n (which is true if C is an n-dimensional sphere for example), then the above theorem implies… CONTINUE READING
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