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arXiv · 2510.26191

Random Diophantine equations of large degree

Tim Browning·Will Sawin
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Abstract

Among the set of hypersurfaces of degree $d$ and dimension $\ell$ defined by the vanishing of a homogeneous polynomial with coefficients $\pm 1$, we investigate the probability that a hypersurface contains a rational point as $d$ and $\ell$ tend to infinity.

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Tim Browning, Will Sawin. 2025-10-30. Random Diophantine equations of large degree. https://arxiv.org/abs/2510.26191

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