论文标题
“ Quasi $ r $ -rank artin问题”的密度
Density of the "quasi $r$-rank Artin problem"
论文作者
论文摘要
对于可能包含负数的有限生成的有限生成的乘法亚组，我们得出了grh的限制，该公式是降低组的索引具有给定值的素数的密度。我们完全对秩一个扭转组的案例进行了分类，该扭力组的密度消失了，而还原组的索引具有给定值是有限的。对于高级组，我们提出了一些部分结果。最后，我们提出了一些示例计算的计算，比较了与$ 10^{10} $计算的近似密度以及由Riemann假设预测的。
For a given finitely generated multiplicative subgroup of the rationals which possibly contain negative numbers, we derive, subject to GRH, formulas for the densities of primes for which the index of the reduction group has a given value. We completely classify the cases of rank one torsion groups for which the density vanishes and the the set of primes for which the index of the reduction group has a given value, is finite. For higher rank groups we propose some partial results. Finally, we propose some computations of examples comparing the approximated density computed with primes up to $10^{10}$ and that predicted by the Riemann Hypothesis.
