论文标题
围绕希尔伯特类多项式的支持问题
Around the support problem for Hilbert class polynomials
论文作者
论文摘要
令$ h_d（t）$表示判别$ d $的假想二次序列的希尔伯特类多项式。我们研究了$ h_d（a）$和$ h_d（b）$ as $ | d |的最大共同分裂的增长率\ to \ for $ a $和$ b $属于各种dedekind域。我们还研究了模块化支持问题：如果除了有限的$ d $几乎有限的每个主要理想划分$ h_d（a）$也将$ h_d（b）$划分，我们对$ a $ a和$ b $怎么说？如果我们用$ t^n-1 $替换$ h_d（t）$，而Dedekind域则是某个数字字段中$ s $ integers的戒指，那么这些是Bugeaud-Corvaja-Zannier，corvaja-Zannier，Corvaja-Zannier和Corrales-Rodrigáñeez-Schoof进行了调查的经典问题。
Let $H_D(T)$ denote the Hilbert class polynomial of the imaginary quadratic order of discriminant $D$. We study the rate of growth of the greatest common divisor of $H_D(a)$ and $H_D(b)$ as $|D| \to \infty$ for $a$ and $b$ belonging to various Dedekind domains. We also study the modular support problem: if for all but finitely many $D$ every prime ideal dividing $H_D(a)$ also divides $H_D(b)$, what can we say about $a$ and $b$? If we replace $H_D(T)$ by $T^n-1$ and the Dedekind domain is a ring of $S$-integers in some number field, then these are classical questions that have been investigated by Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and Corrales-Rodrigáñez-Schoof.
