article epub_ahead yes Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Will Sawin author TiBr department Rational curves via function field analytic number theory project Among the set of hypersurfaces of degree d and dimension defined by the vanishing of a homogeneous polynomial with coefficients in the set {−1, +1}, we investigate the probability that a hypersurface contains a rational point as d and tend to ∞. https://creativecommons.org/licenses/by/4.0/ Oxford University Press2026 eng 0033-5606 1464-3847 2510.2619110.1093/qmath/haag037 Browning TD, Sawin W. Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. 2026. doi:<a href="https://doi.org/10.1093/qmath/haag037">10.1093/qmath/haag037</a> Browning, Timothy D., and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>, haag037, Oxford University Press, 2026, doi:<a href="https://doi.org/10.1093/qmath/haag037">10.1093/qmath/haag037</a>. T. D. Browning and W. Sawin, “Random diophantine equations of large degree,” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026. T.D. Browning, W. Sawin, The Quarterly Journal of Mathematics (2026). Browning TD, Sawin W. 2026. Random diophantine equations of large degree. The Quarterly Journal of Mathematics., haag037. Browning, Timothy D, and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026. <a href="https://doi.org/10.1093/qmath/haag037">https://doi.org/10.1093/qmath/haag037</a>. Browning, T. D., &#38; Sawin, W. (2026). Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href="https://doi.org/10.1093/qmath/haag037">https://doi.org/10.1093/qmath/haag037</a> 231242026-10-12T13:58:16Z2026-10-14T08:49:05Z