论文标题
概率ZETA函数没有负系数的涂料组
Profinite groups in which the probabilistic zeta function has no negative coefficients
论文作者
论文摘要
相关的是有限生成的产品组$ g $，一个正式的dirichlet系列$ p_g（s）= \ sum_ {n \ in \ mathbb n} {a_n（g）}/{n^s} $是关联的$ g的开放子组的晶格的功能。当$ g $是prosoluble时，$（p_g（s））^{ - 1} $的每个系数都是无负的。在本文中，我们讨论了一般案例，并产生了一个非销售示例的％存在，并与同一属性构建了一个非验证有限生成的组$ g $。
To a finitely generated profinite group $G$, a formal Dirichlet series $P_G(s)=\sum_{n \in \mathbb N} {a_n(G)}/{n^s}$ is associated, where $a_n(G)=\sum_{|G:H|=n}μ(H, G)$ and $μ(H,G)$ denotes the Möbius function of the lattice of open subgroups of $G.$ Its formal inverse $P_G^{-1}(s)$ is the probabilistic zeta function of $G$. When $G$ is prosoluble, every coefficient of $(P_G(s))^{-1}$ is nonnegative. In this paper we discuss the general case and we produce % existence of a non-prosoluble example and We construct a non-prosoluble finitely generated group $G$ with the same property.
