Geodesic
Distribution of lattice points on hyperbolic surfaces
Acta Arithmetica, Tome 75 (1996) no. 1, pp. 85-95

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DOI

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.
DOI : 10.4064/aa-75-1-85-95
Keywords: lattice, hyperbolic surface 
Vsevolod Lev. Distribution of lattice points on hyperbolic surfaces. Acta Arithmetica, Tome 75 (1996) no. 1, pp. 85-95. doi: 10.4064/aa-75-1-85-95
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