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Almost prime Pythagorean triples in thin orbits
For the ternary quadratic form Q(x) = x2 + y2 − z2 and a non-zero Pythagorean triple x0 ∈ ℤ3 lying on the cone Q(x) = 0, we consider an orbit 𝒪 = x0Γ of a finitely generated subgroup Γ < SOQ(ℤ) with critical exponent exceeding 1/2.