Distinct Triangle Areas in a Planar Point Set over Finite Fields

نویسنده

Le Anh Vinh

چکیده

Let P be a set of n points in the finite plane 2 q over the finite field q of q elements, where q is an odd prime power. For any s ∈ q , denote by A(P; s) the number of ordered triangles whose vertices in P having area s. We show that if the cardinality of P is large enough then A(P; s) is close to the expected number |P| 3 /q.

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