Rational products of singular moduli

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• 作者：Yuri Bilu^a ; ¹ ; ² ; ^{yuri@math.u-bordeaux.fr" class="auth_mail" title="E-mail the corresponding author} ; Florian Luca^b ; ² ; Amalia Pizarro-Madariaga^c ; ² ; ³
• 关键词：Singular moduli ; Complex multiplication ; André ; &ndash ; Oort ; j-Invariant
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：158
• 期：Complete
• 页码：397-410
• 全文大小：338 K

文摘

We show that with “obvious” exceptions the product of two singular moduli cannot be a non-zero rational number. This gives a totally explicit version of André's 1998 theorem on special points for the hyperbolas x₁x₂=A$x_1{x}_2=A$, where A∈Q$A\in \mathbb{Q}$.