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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 $\mathcal{O}_ε\left(X^{θ+ε}\right)$, with $θ< 2/3$, improving upon results due to Bhargava, Taniguchi, and Thorne. The proof proceeds by relating a certain discriminant-reducing sieve, due to Bhargava, Shankar, a
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