论文标题
整数sn-polynomials家族的算术统计和对群体扭转的应用
Arithmetic statistics of families of integer Sn-polynomials and application to class group torsion
论文作者
论文摘要
我们研究了某些数量领域的某些家庭中分裂素数的分布。第一个也是主要的例子是n族n的n，n的n，高度n的整数多项式一元，然后n等于n，然后让n转到无穷大。我们证明了这个家庭的Chebotarev密度定理的平均版本。特别是，这给出了中央限制定理，其中一些范围内给定的分裂类型的数量。作为应用程序，我们推断出课程组中扭转的一些估计以及平均分支素数的估计值。
We study the distributions of the splitting primes in certain families of number fields. The first and main example is the family Pn,N of integer polynomials monic of degree n with height less or equal then N, and then let N go to infinity. We prove an average version of the Chebotarev Density Theorem for this family. In particular, this gives Central Limit Theorem for the number of primes with given splitting type in some ranges. As an application, we deduce some estimates for the torsion in the class groups and for the average of ramified primes.
