Victor Ahlquist

Averages of Artin characters and their relation to the Davenport--Heilbronn theorem

We bound the error term in the counting function of cubic extensions of $\mathbb{Q}$ by $\mathcal{O}_\epsilon\left(X^{\theta+\epsilon}\right)$, with $\theta<2/3$, improving upon results due to Bhargava, Taniguchi, and Thorne. The proof proceeds by relating a certain discriminant-reducing sieve, due to Bhargava, Shankar...