Close Lattice Points on Circles
نویسندگان
چکیده
We classify the sets of four lattice points that all lie on a short arc of a circle which has its center at the origin; specifically on arcs of length tR on a circle of radius R, for any given t > 0. In particular we prove that any arc of length ( 40 + 40 3 √ 10 )1/3 R on a circle of radius R, with R > √ 65, contains at most three lattice points, whereas we give an explicit infinite family of 4-tuples of lattice points, (ν1,n, ν2,n, ν3,n, ν4,n), each of which lies on an arc of length ( 40 + 40 3 √ 10 )1/3 R 1/3 n +o(1) on a circle of radius Rn.
منابع مشابه
Lattice Points on Circles
We prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.
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