- #1
Peter_Newman
- 155
- 11
Hello,
I am wondering if in an n-ball the number of lattice points is finite.
First, we have a ball which is bounded by the radius. The distance between two lattice points is given by the successive minimum. Theoretically, one could now draw a ball* around each lattice point in the (big) ball that is smaller than the successive minimum. If we assume that there are infinitely many lattice points in the ball, wouldn't that amount to a contradiction, because the ball itself has a finite volume?
Is it even possible to argue like this? Or what would be an argument that the number of lattice points in the ball is finite?
I am wondering if in an n-ball the number of lattice points is finite.
First, we have a ball which is bounded by the radius. The distance between two lattice points is given by the successive minimum. Theoretically, one could now draw a ball* around each lattice point in the (big) ball that is smaller than the successive minimum. If we assume that there are infinitely many lattice points in the ball, wouldn't that amount to a contradiction, because the ball itself has a finite volume?
Is it even possible to argue like this? Or what would be an argument that the number of lattice points in the ball is finite?