论文标题
dirichlet $ l $ functions的第二时刻，角色总和子组和相对班级上的上限
Second moment of Dirichlet $L$-functions, character sums over subgroups and upper bounds on relative class numbers
论文作者
论文摘要
我们证明了均等平均$ L $ - 函数与足够大尺寸字符的子组相关的均值平均值。我们的证明依赖于某些角色的研究总和$ {\ cal a}（p，d）$最近由E. Elma引入。我们获得了$ {\ cal a}（p，d）$的渐近公式，该公式对于任何$ p-1 $ $ d $ $ d $ p，p，d）$持有，以消除对$ d $的大小的先前限制。这解决了Elma论文中提出的问题。我们的证明既取决于统一分布理论的大特征和技术的频率和技术的频率。作为一个应用程序，我们推论以下绑定的$ h_ {
We prove an asymptotic formula for the mean-square average of $L$- functions associated to subgroups of characters of sufficiently large size. Our proof relies on the study of certain character sums ${\cal A}(p,d)$ recently introduced by E. Elma. We obtain an asymptotic formula for ${\cal A}(p,d)$ which holds true for any divisor $d$ of $p-1$ removing previous restrictions on the size of $d$. This anwers a question raised in Elma's paper. Our proof relies both on estimates on the frequency of large character sums and techniques from the theory of uniform distribution. As an application we deduce the following bound $h_{p,d}^- \leq 2\left (\frac{(1+o(1))p}{24}\right )^{m/4}$ on the relative class numbers of the imaginary number fields of conductor $p\equiv 1\mod d$ and degree $m=(p-1)/d$.
