{"year":"2025","citation":{"short":"T.C. Anderson, U.V. Asarhasa, A. Bertelli, F. Gundlach, E.M. O’Dorney, ArXiv:2507.16138 (2025).","chicago":"Anderson, Theresa C., Ufuoma V. Asarhasa, Adam Bertelli, Fabian Gundlach, and Evan M. O’Dorney. “The Structure of the Double Discriminant.” <i>ArXiv:2507.16138</i>, 2025.","apa":"Anderson, T. C., Asarhasa, U. V., Bertelli, A., Gundlach, F., &#38; O’Dorney, E. M. (2025). The structure of the double discriminant. In <i>arXiv:2507.16138</i>.","ieee":"T. C. Anderson, U. V. Asarhasa, A. Bertelli, F. Gundlach, and E. M. O’Dorney, “The structure of the double discriminant,” <i>arXiv:2507.16138</i>. 2025.","mla":"Anderson, Theresa C., et al. “The Structure of the Double Discriminant.” <i>ArXiv:2507.16138</i>, 2025.","ama":"Anderson TC, Asarhasa UV, Bertelli A, Gundlach F, O’Dorney EM. The structure of the double discriminant. <i>arXiv:250716138</i>. Published online 2025.","bibtex":"@article{Anderson_Asarhasa_Bertelli_Gundlach_O’Dorney_2025, title={The structure of the double discriminant}, journal={arXiv:2507.16138}, author={Anderson, Theresa C. and Asarhasa, Ufuoma V. and Bertelli, Adam and Gundlach, Fabian and O’Dorney, Evan M.}, year={2025} }"},"title":"The structure of the double discriminant","_id":"62308","user_id":"100450","publication":"arXiv:2507.16138","external_id":{"arxiv":["2507.16138"]},"language":[{"iso":"eng"}],"abstract":[{"text":"For a polynomial $f(x) = \\sum_{i=0}^n a_i x^i$, we study the double discriminant $DD_{n,k} = \\operatorname{disc}_{a_k} \\operatorname{disc}_x f(x)$. This object has been well studied in algebraic geometry, but has been brought to recent prominence in number theory by its key role in the proof of the Bhargava--van der Waerden theorem. We bridge the knowledge gap for this object by proving an explicit factorization: $DD_{n,k}$ is the product of a square, a cube, and possibly a linear monomial. Our proof is entirely algebraic. We also investigate other aspects of this factorization.","lang":"eng"}],"author":[{"last_name":"Anderson","full_name":"Anderson, Theresa C.","first_name":"Theresa C."},{"full_name":"Asarhasa, Ufuoma V.","last_name":"Asarhasa","first_name":"Ufuoma V."},{"first_name":"Adam","full_name":"Bertelli, Adam","last_name":"Bertelli"},{"id":"100450","first_name":"Fabian","full_name":"Gundlach, Fabian","last_name":"Gundlach"},{"first_name":"Evan M.","last_name":"O'Dorney","full_name":"O'Dorney, Evan M."}],"status":"public","type":"preprint","date_created":"2025-11-26T08:18:33Z","date_updated":"2025-11-26T08:21:27Z"}