Distribution of lattice points on hyperbolic surfaces
Volume 75 / 1996
Acta Arithmetica 75 (1996), 85-95 DOI: 10.4064/aa-75-1-85-95
Let two lattices $Λ', Λ'' ⊂ ℝ^s$ have the same number of points on each hyperbolic surface $|x₁...x_s| = C$. We investigate the case when Λ', Λ'' are sublattices of $ℤ^s$ of the same prime index and show that then Λ' and Λ'' must coincide up to renumbering the coordinate axes and changing their directions.