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arXiv · 1605.05265

Almost Primes in Thin Orbits of Pythagorean Triangles

Max Ehrman
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Abstract

Let $F=x^2+y^2-z^2$, $x_0 \in \mathbb{Z}^3$ primitive with $F(x_0)=0$, and $Γ\leq SO_F(\mathbb{Z})$ be a finitely generated thin subgroup. We consider the resulting thin orbits of Pythagorean triples $x_0 \cdot Γ$ - specifically which hypotenuses, areas, and products of all three coordinates arise. We produce infinitely many $R$-almost primes in these three cases whenever $Γ$ has exponent $δ_Γ>δ_0(R)$ for explicit $R$, $δ_0$.

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Max Ehrman. 2016-05-17. Almost Primes in Thin Orbits of Pythagorean Triangles. https://arxiv.org/abs/1605.05265

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