论文标题
椭圆曲线的扭转组$ \ mathbb {q}（μ__{p^{\ infty}}）$
Torsion groups of elliptic curves over $\mathbb{Q}(μ_{p^{\infty}})$
论文作者
论文摘要
令$ e/\ mathbb {q} $为椭圆曲线，而$ p \ in \ {5,7,11 \} $为prime。我们确定$ e（\ mathbb {q}（ζ_{p}））_ {tors} $的可能性。此外，我们确定$ e（\ mathbb {q}（ζ_{16}））的所有可能性_ {tors} $和$ e（\ Mathbb {q}（ζ_{27}）（ζ_{27}））_ _ {tors} $。使用这些结果，我们能够确定$ e（\ Mathbb {q}（μ__{p^{\ infty}}}）））_ {tors} $的可能性。
Let $E/\mathbb{Q}$ be an elliptic curve and $p \in \{5,7,11 \}$ be a prime. We determine the possibilities for $E(\mathbb{Q}(ζ_{p}))_{tors}$. Additionally, we determine all the possibilities for $E(\mathbb{Q}(ζ_{16}))_{tors}$ and $E(\mathbb{Q}(ζ_{27}))_{tors}$. Using these results we are able to determine the possibilities for $E(\mathbb{Q}(μ_{p^{\infty}}))_{tors}$.
