# Lattice points inside a (n-dimensional) tetrahedron

Hi, overflowers.

I was interested in a sharp lower bound for the number of lattice points (say, integral lattice points) inside the tetrahedron defined by the coordinate hyperplanes and $x_1/a_1+...+x_n/a_n=1$, with $a_1,...,a_n \in {\mathbf R}$ (rational coefficients may be enough, although I think it doesn't help a lot).

I know there is a good upper bound from the "rough part" of so-called GLY conjecture, which has already been proved by Yau & Zhang; but I just can't find a similar result for lower bounds.

Thanks a lot.

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