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- W4280513642 abstract "In this paper, we prove the assertion that the number of monic cubic polynomials $F(x) = x^3 + a_2 x^2 + a_1 x + a_0$ with integer coefficients and irreducible, Galois over ${mathbb {Q}}$ satisfying $max {|a_2|, |a_1|, |a_0|} leq X$ is bounded from above by $O(X (log X)^2)$ . We also count the number of abelian monic binary cubic forms with integer coefficients up to a natural equivalence relation ordered by the so-called Bhargava–Shankar height. Finally, we prove an assertion characterizing the splitting field of 2-torsion points of semi-stable abelian elliptic curves." @default.
- W4280513642 created "2022-05-22" @default.
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- W4280513642 date "2022-03-01" @default.
- W4280513642 modified "2023-10-03" @default.
- W4280513642 title "On monic abelian cubics" @default.
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- W4280513642 doi "https://doi.org/10.1112/s0010437x22007369" @default.
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