A motivic secondary term for counting S3-cubic extensions

Let N₃(X) be the number of cubic extensions K/Q of absolute discriminant <= X. In 1971, Davenport and Heilbronn showed that N₃(X) = cX + o(X) for some constant c. More recently in 2012, work of Bhargava, Shankar, and Tsimerman gives a second order term: they showed N₃(X) = cX + c' X^5/6 + o(X^5/6). In 2025, Kural proved the same secondary term in the function field case; in this talk I'll discuss joint work with Vakil in which we prove the analogous motivic statement in the Grothendieck ring of stacks.