Bateman-Horn, polynomial Chowla and the Hasse principle with probability

article Bateman-Horn, polynomial Chowla and the Hasse principle with probability epub_ahead yes Timothy D Browning author 35827D50-F248-11E8-B48F-1D18A9856A870000-0002-8314-0177 Efthymios Sofos author Joni Teräväinen author TiBr department New frontiers of the Manin conjecture project With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree 𝑑 polynomials 𝑓∈ℤ⁢[𝑡] that are ordered by height. This allows us to establish averaged versions of the Bateman–Horn conjecture, the polynomial Chowla conjecture and to address a basic question about the integral Hasse principle for norm form equations. Moreover, we are able to quantify the error term in the asymptotics and the size of the exceptional set of 𝑓, both with arbitrary logarithmic power savings. De Gruyter2026 eng Journal für die reine und angewandte Mathematik 0075-4102 1435-5345 2212.1037310.1515/crelle-2026-0062 Browning TD, Sofos E, Teräväinen J. Bateman-Horn, polynomial Chowla and the Hasse principle with probability. Journal für die reine und angewandte Mathematik. 2026. doi:<a href="https://doi.org/10.1515/crelle-2026-0062">10.1515/crelle-2026-0062</a> Browning, Timothy D., et al. “Bateman-Horn, Polynomial Chowla and the Hasse Principle with Probability.” Journal Für Die Reine Und Angewandte Mathematik, De Gruyter, 2026, doi:<a href="https://doi.org/10.1515/crelle-2026-0062">10.1515/crelle-2026-0062</a>. T.D. Browning, E. Sofos, J. Teräväinen, Journal Für Die Reine Und Angewandte Mathematik (2026). T. D. Browning, E. Sofos, and J. Teräväinen, “Bateman-Horn, polynomial Chowla and the Hasse principle with probability,” Journal für die reine und angewandte Mathematik. De Gruyter, 2026. Browning TD, Sofos E, Teräväinen J. 2026. Bateman-Horn, polynomial Chowla and the Hasse principle with probability. Journal für die reine und angewandte Mathematik. Browning, Timothy D, Efthymios Sofos, and Joni Teräväinen. “Bateman-Horn, Polynomial Chowla and the Hasse Principle with Probability.” Journal Für Die Reine Und Angewandte Mathematik. De Gruyter, 2026. <a href="https://doi.org/10.1515/crelle-2026-0062">https://doi.org/10.1515/crelle-2026-0062</a>. Browning, T. D., Sofos, E., & Teräväinen, J. (2026). Bateman-Horn, polynomial Chowla and the Hasse principle with probability. Journal Für Die Reine Und Angewandte Mathematik. De Gruyter. <a href="https://doi.org/10.1515/crelle-2026-0062">https://doi.org/10.1515/crelle-2026-0062</a> 228212026-09-06T22:01:58Z2026-09-09T13:28:45Z