论文标题
Chebyshev在二面体和广义的四元基金会中的偏见
Chebyshev's bias in dihedral and generalized quaternion Galois groups
论文作者
论文摘要
我们研究了与二面体$ d_ {2n} $或（概括性的）quaternion $ \ mathbb h_ {2n} $的两点订单的dihedral $ d_ {2n} $的Galois组的Frobenius元素分布的不平等。本着Fiorilli和Jouve Arxiv的最新工作的精神：2001.05428，我们在自然假设下，在水平方面，某些延伸的家庭研究，在水平方面，该程度是固定的，在垂直方面，程度为无限。我们的主要贡献在延伸家族中揭示了一种现象，为此提供了数值证据：Artin L功能的真正零有时对Frobenius元素的分布有根本的影响。
We study the inequities in the distribution of Frobenius elements in Galois extensions of the rational numbers with Galois groups that are either dihedral $D_{2n}$ or (generalized) quaternion $\mathbb H_{2n}$ of two-power order. In the spirit of recent work of Fiorilli and Jouve arXiv:2001.05428, we study, under natural hypotheses, some families of such extensions, in a horizontal aspect, where the degree is fixed, and in a vertical aspect, where the degree goes to infinity. Our main contribution uncovers in families of extensions a phenomenon, for which Ng gave numerical evidence : real zeros of Artin L-functions sometimes have a radical influence on the distribution of Frobenius elements.
