论文标题
打破了班级生成集的界限的4个障碍
Breaking the 4 barrier for the bound of a generating set of the class group
论文作者
论文摘要
令$ k $为$ n $的范围，具有绝对值$δ$的判别。在普遍的Riemann假设的有效性的假设下，我们提供了一种新算法来计算$ k $的班级组的一组发电机，并证明该集合中的理想的规范是$ \ leq（4-1/（2N））\ log^2δ$，除了$ n \ n \ n \ n \ le $ n \ le q led $ n \ led $ n \ led $ n \ led $ n \ led $ n \ led $ n \ led $ n \ led $ n \ led $ n \ le n \ le n \ le q le q les $ n。对于这些字段，结论以稍大的限制$（4-1/（2n）+1/（2n^2））\ log^2δ$。当$ \ Mathcal c \！\ ell $的基数奇怪时，界限提高到$（4-2/（3n））\ log^2δ$，同样有限的许多例外$ n \ leq 4 $，以及$（4-2/（3N）+3/（8n^2））\ log^2）\ log^2 $。
Let $K$ be a field of degree $n$ and discriminant with absolute value $Δ$. Under the assumption of the validity of the Generalized Riemann Hypothesis, we provide a new algorithm to compute a set of generators of the class group of $K$ and prove that the norm of the ideals in that set is $\leq (4-1/(2n))\log^2Δ$, except for a finite number of fields of degree $n\leq 4$. For those fields, the conclusion holds with the slightly larger limit $(4-1/(2n)+1/(2n^2))\log^2Δ$. When the cardinality of $\mathcal C\!\ell$ is odd the bounds improve to $(4-2/(3n))\log^2Δ$, again with finitely many exceptions in degree $n\leq 4$, and to $(4-2/(3n)+3/(8n^2))\log^2Δ$ without exceptions.
