Liouville function, von Mangoldt function, and norm forms at random binary forms

article Liouville function, von Mangoldt function, and norm forms at random binary forms epub_ahead yes Yijie Diao author 7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b0000-0002-4989-5330 TiBr department GradSch department We analyze the average behavior of various arithmetic functions at the values of degree 𝑑 binary forms ordered by height, with probability 1. This approach yields averaged versions of the Chowla conjecture and the Bateman–Horn conjecture for random binary forms. Furthermore, we show that the rational Hasse principle holds for almost all Châtelet varieties defined by a fixed norm form of degree 𝑒 and by varying binary forms of fixed degree 𝑑, provided 𝑒 divides 𝑑. This proves an average version of a conjecture of Colliot-Thélène. https://creativecommons.org/licenses/by/4.0/ Cambridge University Press2026 eng Glasgow Mathematical Journal 0017-0895 1469-509X 2506.1806510.1017/s0017089526101074 1-34 Diao, Yijie. “Liouville Function, von Mangoldt Function, and Norm Forms at Random Binary Forms.” Glasgow Mathematical Journal, Cambridge University Press, 2026, pp. 1–34, doi:<a href="https://doi.org/10.1017/s0017089526101074">10.1017/s0017089526101074</a>. Y. Diao, “Liouville function, von Mangoldt function, and norm forms at random binary forms,” Glasgow Mathematical Journal. Cambridge University Press, pp. 1–34, 2026. Diao Y. 2026. Liouville function, von Mangoldt function, and norm forms at random binary forms. Glasgow Mathematical Journal., 1–34. Diao Y. Liouville function, von Mangoldt function, and norm forms at random binary forms. Glasgow Mathematical Journal. 2026:1-34. doi:<a href="https://doi.org/10.1017/s0017089526101074">10.1017/s0017089526101074</a> Diao, Yijie. “Liouville Function, von Mangoldt Function, and Norm Forms at Random Binary Forms.” Glasgow Mathematical Journal. Cambridge University Press, 2026. <a href="https://doi.org/10.1017/s0017089526101074">https://doi.org/10.1017/s0017089526101074</a>. Diao, Y. (2026). Liouville function, von Mangoldt function, and norm forms at random binary forms. Glasgow Mathematical Journal. Cambridge University Press. <a href="https://doi.org/10.1017/s0017089526101074">https://doi.org/10.1017/s0017089526101074</a> Y. Diao, Glasgow Mathematical Journal (2026) 1–34. 226442026-08-04T06:15:04Z2026-08-04T06:28:01Z